When I apply the following replacement

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

the result is


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 Hanlon Mar 8 '17 at 3:23

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  • 3
    $\begingroup$ Try PowerExpand[]. $\endgroup$ – Anjan Kumar Mar 6 '17 at 23:11
  • $\begingroup$ @AnjanKumar Thank you, it works. $\endgroup$ – 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)

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

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

Or more generally:

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

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


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