I think Alpha tried to give nice answers.  I've never used
Mathematica, but I suspect it would be a little more rigorous about
assumptions, as Maple is and as we should be.

I should have mentioned that I can force Maple to give
x**(21/4)*y**(7/4) by doing
simplify(x**4*y*sqrt(x*y)*sqrt(x*sqrt(x*y)), power, symbolic).

If the combination is valid (and if it's not we should reconsider how
we do auto-combination in Mul.flatten), then powsimp should be able to
do it. I suspect that Maple just isn't smart enough to do this piece
of non-trivial simplification, or else I do not know the correct
function to pass it to.

Aaron Meurer

On Sun, Aug 14, 2011 at 3:35 AM, Chris Smith <[email protected]> wrote:
> On Sun, Aug 14, 2011 at 2:26 PM, Aaron Meurer <[email protected]> wrote:
>> Mathematica or WolframAlpha?
>
> Alpha. It gives the expression unchanged and then the expression as it
> would appear if x and y were positive. Because of autoexpansion of
> positive bases under Rationals, sympy can't presently show the
> expression as `(x**21*y**7)**(1/4)`.
>
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