Question

How do you prove$(a^m)^{-1} = (a^{-1})^m$ for a being any non-zero real and m being a positive integer from the axioms of real numbers?

score 143 · Answer 1 · 2015-10-24 20:20:04

How do you prove$(a^m)^{-1} = (a^{-1})^m$ for a being any non-zero real and m being a positive integer from the axioms of real numbers?

score 109 · Answer 2 · 2015-10-28 21:46:04

109

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score 1.6k · Answer 3 · 2026-03-24 00:24:28

1.6k

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Understanding axioms of neighbourhoods in topological spaces

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score 77 · Answer 4 · 2026-03-12 14:10:32

77

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If the product of two numbers is nonnegative than either both are nonnegative or both are nonpositive

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score 195 · Answer 5 · 2026-03-29 16:14:58

195

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Existence of Axioms

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1.3k

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How to prove Playfair's axiom or Euclid's parallel postulate without using angle measure

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score 89 · Answer 7 · 2015-11-04 15:29:30

89

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Does a curve violate the first postulate of Euclidean Geometry?

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score 1.8k · Answer 8 · 2015-11-05 02:11:09

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score 57 · Answer 9 · 2026-03-30 00:47:33

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score 919 · Answer 10 · 2026-03-28 17:01:30

919

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Axioms of Affine Space

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score 391 · Answer 11 · 2026-03-26 17:40:39

391

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score 51 · Answer 12 · 2015-11-08 17:35:14

51

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score 130 · Answer 13 · 2015-11-10 01:11:38

130

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do the line order axioms imply the plane separation axiom?

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score 474 · Answer 14 · 2026-03-27 13:20:05

474

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score 55 · Answer 15 · 2015-11-12 17:27:51

55

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$z \cap x$ denotes a set whose existence is proved using the axiom of replacement?

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List Question

How do you prove$(a^m)^{-1} = (a^{-1})^m$ for a being any non-zero real and m being a positive integer from the axioms of real numbers?

How to show $a+b=b+a$ correctly?

Understanding axioms of neighbourhoods in topological spaces

If the product of two numbers is nonnegative than either both are nonnegative or both are nonpositive

Existence of Axioms

How to prove Playfair's axiom or Euclid's parallel postulate without using angle measure

Does a curve violate the first postulate of Euclidean Geometry?

Prove if $x<y$ then $x+z<y+z$

Field property proof

Axioms of Affine Space

Modal logic of contingency and necessity operators?

Logical formula deducing

do the line order axioms imply the plane separation axiom?

How do inconsistent arithmetics get around Gödel incompleteness?

$z \cap x$ denotes a set whose existence is proved using the axiom of replacement?

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