Problem with symbol power [closed]

When I apply the following replacement

z^(21/5) /. z -> x^-5

the result is

(1/x^5)^(21/5)

At the level of symbol, obviously this is $x^{-21}$, but I try FullSimplify, Expand, Factor, ExpandAll, ..., and I could not simplify the result to $x^{-21}$. Anyone know why? and how to simplify expressions contains rational powers like this?

closed as off-topic by m_goldberg, LLlAMnYP, happy fish, MarcoB, Bob HanlonMar 8 '17 at 3:23

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• Try PowerExpand[]. – Anjan Kumar Mar 6 '17 at 23:11
• @AnjanKumar Thank you, it works. – Wenzhe Mar 6 '17 at 23:14

This does not evaluate because (1/x^5)^(21/5) != 1/x^21 for all x in the complex plane:

With[{x = -1},
(1/x^5)^(21/5) == (1/x^21)
]
False

You can simplify over a restricted domain to get what you want:

FullSimplify[(1/x^5)^(21/5), x > 0]
1/x^21

Or more generally:

FullSimplify[(1/x^5)^(21/5), -π/5 <= Arg[x] < π/5]
1/x^21

You might also be interested in Surd if you prefer the real valued root over the principal valued one.