# Natural-Number Powers and Principal Square Roots

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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261003-r01-power-root-foundations · 2026-10-03 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-12)^0 exactly.

View answer and explanation1

(-12)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0001/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 2. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-11)^1 exactly.

View answer and explanation-11

(-11)^1=-11. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0002/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 3. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-10)^2 exactly.

View answer and explanation100

(-10)^2=100. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0003/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 4. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-9)^3 exactly.

View answer and explanation-729

(-9)^3=-729. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0004/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 5. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-8)^4 exactly.

View answer and explanation4096

(-8)^4=4096. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0005/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 6. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-7)^5 exactly.

View answer and explanation-16807

(-7)^5=-16807. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0006/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 7. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-6)^0 exactly.

View answer and explanation1

(-6)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0007/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 8. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-5)^1 exactly.

View answer and explanation-5

(-5)^1=-5. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0008/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 9. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-4)^2 exactly.

View answer and explanation16

(-4)^2=16. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0009/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 10. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-3)^3 exactly.

View answer and explanation-27

(-3)^3=-27. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0010/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 11. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-2)^4 exactly.

View answer and explanation16

(-2)^4=16. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0011/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 12. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (-1)^5 exactly.

View answer and explanation-1

(-1)^5=-1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0012/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 13. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (0)^0 exactly.

View answer and explanation1

(0)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0013/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 14. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (0)^1 exactly.

View answer and explanation0

(0)^1=0. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0014/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 15. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (2)^2 exactly.

View answer and explanation4

(2)^2=4. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0015/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 16. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (3)^3 exactly.

View answer and explanation27

(3)^3=27. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0016/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 17. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (4)^4 exactly.

View answer and explanation256

(4)^4=256. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0017/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 18. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (5)^5 exactly.

View answer and explanation3125

(5)^5=3125. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0018/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 19. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (6)^0 exactly.

View answer and explanation1

(6)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0019/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 20. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (7)^1 exactly.

View answer and explanation7

(7)^1=7. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0020/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 21. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (8)^2 exactly.

View answer and explanation64

(8)^2=64. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0021/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 22. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (9)^3 exactly.

View answer and explanation729

(9)^3=729. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0022/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 23. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (10)^4 exactly.

View answer and explanation10000

(10)^4=10000. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0023/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 24. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (11)^5 exactly.

View answer and explanation161051

(11)^5=161051. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0024/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 25. Exact Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (12)^0 exactly.

View answer and explanation1

(12)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0025/)

Natural-number powers and principal square roots · qf-natural-power-exact · candidate





## 26. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (0)^0 positive, negative, or zero?

View answer and explanationpositive

(0)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0026/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 27. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-9)^1 positive, negative, or zero?

View answer and explanationnegative

(-9)^1=-9. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0027/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 28. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-8)^2 positive, negative, or zero?

View answer and explanationpositive

(-8)^2=64. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0028/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 29. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-7)^3 positive, negative, or zero?

View answer and explanationnegative

(-7)^3=-343. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0029/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 30. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-6)^4 positive, negative, or zero?

View answer and explanationpositive

(-6)^4=1296. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0030/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 31. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-5)^5 positive, negative, or zero?

View answer and explanationnegative

(-5)^5=-3125. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0031/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 32. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-4)^6 positive, negative, or zero?

View answer and explanationpositive

(-4)^6=4096. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0032/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 33. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-3)^0 positive, negative, or zero?

View answer and explanationpositive

(-3)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0033/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 34. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-2)^1 positive, negative, or zero?

View answer and explanationnegative

(-2)^1=-2. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0034/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 35. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (-1)^2 positive, negative, or zero?

View answer and explanationpositive

(-1)^2=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0035/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 36. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (0)^3 positive, negative, or zero?

View answer and explanationzero

(0)^3=0. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0036/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 37. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (1)^4 positive, negative, or zero?

View answer and explanationpositive

(1)^4=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0037/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 38. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (2)^5 positive, negative, or zero?

View answer and explanationpositive

(2)^5=32. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0038/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 39. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (3)^6 positive, negative, or zero?

View answer and explanationpositive

(3)^6=729. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0039/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 40. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (4)^0 positive, negative, or zero?

View answer and explanationpositive

(4)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0040/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 41. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (5)^1 positive, negative, or zero?

View answer and explanationpositive

(5)^1=5. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0041/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 42. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (6)^2 positive, negative, or zero?

View answer and explanationpositive

(6)^2=36. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0042/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 43. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (7)^3 positive, negative, or zero?

View answer and explanationpositive

(7)^3=343. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0043/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 44. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (8)^4 positive, negative, or zero?

View answer and explanationpositive

(8)^4=4096. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0044/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 45. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (9)^5 positive, negative, or zero?

View answer and explanationpositive

(9)^5=59049. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0045/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 46. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (10)^6 positive, negative, or zero?

View answer and explanationpositive

(10)^6=1000000. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0046/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 47. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (11)^0 positive, negative, or zero?

View answer and explanationpositive

(11)^0=1. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0047/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 48. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (12)^1 positive, negative, or zero?

View answer and explanationpositive

(12)^1=12. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0048/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 49. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (13)^2 positive, negative, or zero?

View answer and explanationpositive

(13)^2=169. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0049/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 50. Sign of a Natural-Number Power

For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Is (14)^3 positive, negative, or zero?

View answer and explanationpositive

(14)^3=2744. At exponent zero the empty product is 1; for positive exponents use the base sign and exponent parity. This convention is not a rule for limits.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0050/)

Natural-number powers and principal square roots · qf-natural-power-sign · candidate





## 51. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √0.

View answer and explanation0

0²=0 and 0≥0, so the principal square root is 0; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0051/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 52. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √1.

View answer and explanation1

1²=1 and 1≥0, so the principal square root is 1; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0052/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 53. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √4.

View answer and explanation2

2²=4 and 2≥0, so the principal square root is 2; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0053/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 54. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √9.

View answer and explanation3

3²=9 and 3≥0, so the principal square root is 3; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0054/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 55. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √16.

View answer and explanation4

4²=16 and 4≥0, so the principal square root is 4; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0055/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 56. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √25.

View answer and explanation5

5²=25 and 5≥0, so the principal square root is 5; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0056/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 57. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √36.

View answer and explanation6

6²=36 and 6≥0, so the principal square root is 6; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0057/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 58. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √49.

View answer and explanation7

7²=49 and 7≥0, so the principal square root is 7; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0058/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 59. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √64.

View answer and explanation8

8²=64 and 8≥0, so the principal square root is 8; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0059/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 60. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √81.

View answer and explanation9

9²=81 and 9≥0, so the principal square root is 9; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0060/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 61. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √100.

View answer and explanation10

10²=100 and 10≥0, so the principal square root is 10; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0061/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 62. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √121.

View answer and explanation11

11²=121 and 11≥0, so the principal square root is 11; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0062/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 63. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √144.

View answer and explanation12

12²=144 and 12≥0, so the principal square root is 12; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0063/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 64. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √169.

View answer and explanation13

13²=169 and 13≥0, so the principal square root is 13; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0064/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 65. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √196.

View answer and explanation14

14²=196 and 14≥0, so the principal square root is 14; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0065/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 66. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √225.

View answer and explanation15

15²=225 and 15≥0, so the principal square root is 15; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0066/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 67. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √256.

View answer and explanation16

16²=256 and 16≥0, so the principal square root is 16; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0067/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 68. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √289.

View answer and explanation17

17²=289 and 17≥0, so the principal square root is 17; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0068/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 69. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √324.

View answer and explanation18

18²=324 and 18≥0, so the principal square root is 18; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0069/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 70. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √361.

View answer and explanation19

19²=361 and 19≥0, so the principal square root is 19; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0070/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 71. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √400.

View answer and explanation20

20²=400 and 20≥0, so the principal square root is 20; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0071/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 72. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √441.

View answer and explanation21

21²=441 and 21≥0, so the principal square root is 21; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0072/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 73. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √484.

View answer and explanation22

22²=484 and 22≥0, so the principal square root is 22; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0073/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 74. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √529.

View answer and explanation23

23²=529 and 23≥0, so the principal square root is 23; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0074/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 75. Principal Square Root of a Perfect Square

Using the principal square root on the nonnegative reals, find the exact nonnegative value of √576.

View answer and explanation24

24²=576 and 24≥0, so the principal square root is 24; it is a single value rather than two signed branches.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0075/)

Natural-number powers and principal square roots · qf-principal-square-root-exact · candidate





## 76. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-12 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-12 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0076/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 77. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-11 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-11 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0077/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 78. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-10 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-10 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0078/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 79. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-9 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-9 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0079/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 80. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-8 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-8 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0080/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 81. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-7 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-7 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0081/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 82. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-6 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-6 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0082/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 83. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-5 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-5 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0083/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 84. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-4 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-4 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0084/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 85. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-3 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-3 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0085/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 86. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-2 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-2 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0086/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 87. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=-1 belong to its domain? Answer Yes or No.

View answer and explanationNo

r=-1 does not satisfy r≥0, so the answer is No. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0087/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 88. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=0 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=0 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0088/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 89. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=1 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=1 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0089/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 90. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=2 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=2 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0090/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 91. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=3 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=3 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0091/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 92. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=4 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=4 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0092/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 93. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=5 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=5 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0093/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 94. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=6 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=6 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0094/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 95. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=7 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=7 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0095/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 96. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=8 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=8 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0096/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 97. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=9 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=9 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0097/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 98. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=10 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=10 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0098/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 99. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=11 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=11 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0099/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate





## 100. Real Domain of the Principal Square Root

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=12 belong to its domain? Answer Yes or No.

View answer and explanationYes

r=12 satisfies r≥0, so the answer is Yes. A software convention returning zero for a negative input is outside this definition.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r01-power-root-0100/)

Natural-number powers and principal square roots · qf-principal-square-root-domain · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r01-power-root-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261003-r01-power-root-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r01-power-root-foundations/validation-report.json)