0
$\begingroup$

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?

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – m_goldberg, LLlAMnYP, happy fish, MarcoB, Bob Hanlon
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 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
4
$\begingroup$

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.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.