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I would expect the command

FullSimplify[(a b)^p == a^p b^p, {a, b, p} > 0]

to evaluate to True. But it doesn't; it just returns the original equation. Why not?

Also, is there any way that I can "force" Mathematica to realize that exponents distribute over products (when everything's positive) when it's simplifying expressions, so that I can check more complicated expressions for equivalence?

v14.0

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    $\begingroup$ Or you can just use PowerExpand which has the needed assumptions builtin PowerExpand[(a b)^p]==a^p b^p gives True $\endgroup$ Commented Sep 1 at 1:50
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    $\begingroup$ Use \[VectorGreater] rather than >. $\endgroup$ Commented Sep 1 at 9:24
  • $\begingroup$ Is it easier to remember "with several conditions just use AND between them" like this: FullSimplify[(a b)^p==a^p b^p,a>0&&b>0&&p>0] than it is to remember the details of PowerExpand does or does not do or to discover something you and I have likely never seen or understood like And@@Thread[...] $\endgroup$ Commented Sep 1 at 12:11

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Your assumptions {a, b, p} > 0 are wrongly written.

FullSimplify[(a b)^p == a^p b^p, And @@ Thread[{a, b, p} > 0]]

True
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