Re: FullSimplify doesn't simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg32775] Re: FullSimplify doesn't simplify
• From: Steve Luttrell <luttrell at signal.qinetiq.com>
• Date: Sat, 9 Feb 2002 05:11:48 -0500 (EST)
• Organization: QinetiQ
• References: <a404nb\$bqk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Try this one, which gives the result {Sqrt[6], -Sqrt[6]}:

{(x y)^n, x^n y^n} /. {x -> -2, y -> -3, n -> 1/2}

The two expressions evaluate to different results because fractional
powers have multiple values.

On the other hand the following gives the result True, because you
explicitly state that n is an integer (i.e. not a fractional) power:

Simplify[(x y)^n == x^n y^n, n \[Element] Integers]

Steve Luttrell

"Ken Morgan" <kmorga51 at calvin.edu> wrote in
news:a404nb\$bqk\$1 at smc.vnet.net:

> 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?

```

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