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Re: FullSimplify doesn't simplify

  • To: mathgroup at
  • Subject: [mg32778] Re: FullSimplify doesn't simplify
  • From: "John Doty" <jpd at>
  • Date: Sat, 9 Feb 2002 05:11:54 -0500 (EST)
  • References: <a404nb$bqk$>
  • Sender: owner-wri-mathgroup at

In article <a404nb$bqk$1 at>, "Ken Morgan" <kmorga51 at>

> 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?


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

Out[1]= False

It's true in some common special cases:

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

Out[2]= True

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

Out[3]= True

If you like living dangerously you can use PowerExpand:

In[4]:= PowerExpand[(x y)^n == (x^n)(y^n)]

Out[4]= True

Beware, however, that PowerExpand's transformations are not valid in

| John Doty		"You can't confuse me, that's my job."
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