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R0055-28246 · q-20261003-r01-power-root-0046
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?
G001 — 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?Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-natural-power-sign, power_sign]
After
derived = [[power_sign_label]]
Conditions: none
List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.
Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001
Before
Legacy power ORIGINAL multiply1 := mul(1, 10)
After
Legacy power ORIGINAL multiply1 = 10
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
Legacy power ORIGINAL multiply2 := mul(10, 10)
After
Legacy power ORIGINAL multiply2 = 100
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
Legacy power ORIGINAL multiply3 := mul(100, 10)
After
Legacy power ORIGINAL multiply3 = 1000
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
Legacy power ORIGINAL multiply4 := mul(1000, 10)
After
Legacy power ORIGINAL multiply4 = 10000
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
Legacy power ORIGINAL multiply5 := mul(10000, 10)
After
Legacy power ORIGINAL multiply5 = 100000
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S005
Before
Legacy power ORIGINAL multiply6 := mul(100000, 10)
After
Legacy power ORIGINAL multiply6 = 1000000
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S006
Before
source roles = [10, 6, empty_product]
After
derived = [1000000, positive]
Conditions: none
The n0 empty product is1,including0^0=1 in THIS algebraic setting,not a limit rule.For n>0 a zero base gives0;otherwise sign follows base sign and exponent parity.All BigInt results remain exact without derived SAFE/1e8 clipping.
Rule: Legacy_power_ALL_n_products_EMPTYproduct_n0_and_sign_parity · Uses: G001, S007
S008 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.S007 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply6 with exact rational arithmetic, not rounded decimals.S006 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply5 with exact rational arithmetic, not rounded decimals.S005 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply4 with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply3 with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply2 with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute Legacy power ORIGINAL multiply1 with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.positive
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: b516b576e1057d954eb2c47461c71f9ded909828928a491fab823d5093b015d4candidate record SHA-256: 298b8c6385c45a606f967c963e5c3551739613aa8c2b9c4989a84145f3ef8cbfsemantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4eLean: NOT_RUN · human review: NOT_PERFORMED