perplexus.info :: Just Math : Commutative Exponentiation

Commutative Exponentiation (Posted on 2017-07-07)

In general exponentiation is not commutative. However most people are aware of the pair 2 and 4 as a pair of unequal numbers for which exponentiation is commutative.

Show that there are an infinite number of pairs of unequal numbers for which exponentiation is commutative.

Go further and show that there are an infinite number of pairs of unequal rational numbers for which exponentiation is commutative.

See The Solution Submitted by Brian Smith

Rating: 4.0000 (1 votes)

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One unusual solution

| Comment 5 of 7 |

-2 and -4 work

(-2)^(-4) = (-4)^(-2) = 1/16

I don't know of any other negative numbers that work.

Posted by Steve Herman on 2017-07-07 19:15:29

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