Re: Simplify exponents in output

• To: mathgroup at smc.vnet.net
• Subject: [mg99227] Re: Simplify exponents in output
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Thu, 30 Apr 2009 06:23:33 -0400 (EDT)
• References: <gt90lf\$l29\$1@smc.vnet.net>

```This question has been asked and answered many times before in this
forum.

Part of the answer can be found in this Mathematica doc page: tutorial/
FunctionsThatDoNotHaveUniqueValues

Underlying problem is that -1^(1/3) doesn't have -1 as the sole
answer. The complex numbers 1/2 + I 1/2 Sqrt[3] and 1/2 - I 1/2 Sqrt
[3] work as well.

So if x would equal -1, x^9 equals -1 and (x^9)^(1/3) would be (-1)^
(1/3) which has the above three expansions, whereas (-1)^3 only yields
-1. If you wanted to be mathematically precise, you wouldn't want to
equate the outcomes of both routes as the solution sets are not the
same.

If you declare that x is a positive real, Mathematica will simplify
it:

In[457]:= Simplify[(x^9)^(1/3), Assumptions -> {x > 0}]

Out[457]= x^3

Cheers -- Sjoerd

On Apr 29, 9:46 am, davef <davidfrick2... at yahoo.com> wrote:
> When I attempt to solve the following  in Mathematica:
>
> (64 x^9)^(1/3)
>
> I get this:
>
> 4 (x^9)^1/3
>
> Why don't I get:
>
> 4x^3
>
> IOW, why doesn't Mathematica simplify the variable under the radical in t=
he output?
>
> I am using Mathematica 7.
>
> Thanks.

```

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