       Re: FullSimplify doesn't simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg32778] Re: FullSimplify doesn't simplify
• From: "John Doty" <jpd at w-d.org>
• Date: Sat, 9 Feb 2002 05:11:54 -0500 (EST)
• References: <a404nb\$bqk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <a404nb\$bqk\$1 at smc.vnet.net>, "Ken Morgan" <kmorga51 at calvin.edu>
wrote:

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

Sure:

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

Out= False

It's true in some common special cases:

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

Out= True

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

Out= True

If you like living dangerously you can use PowerExpand:

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

Out= True

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

--
| John Doty		"You can't confuse me, that's my job."
| Home: jpd at w-d.org
| Work: jpd at space.mit.edu

```

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