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Re: FullSimplify doesn't simplify

"Ken Morgan" <kmorga51 at> wrote:

> Does anyone know why Mathematica doesn't simplify the following to True?
> In[1] := FullSimplify[(x y)^n == (x^n)(y^n)]
> Out[1] := (x y)^n == (x^n)(y^n)
> Are there cases where this is not true?
> Thanks,
> Ken Morgan
> kmorga51 at

It is apparently not true when both x and y are negative and n is not an integer:

In[1]:= (x y)^n - (x^n)(y^n) /. {x->-1, y->-2, n->1/2}

Out[1]= 2 Sqrt[2]

In[2]:= FullSimplify[(x y)^n - (x^n)(y^n), n \[Element] Integers]

Out[2]= 0

In[3]:= FullSimplify[(x y)^n - (x^n)(y^n), x>0]

Out[3]= 0

Wolfram Research.

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