Re: Simplify exponents in output

• To: mathgroup at smc.vnet.net
• Subject: [mg99233] Re: Simplify exponents in output
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Thu, 30 Apr 2009 06:24:39 -0400 (EDT)

```On 4/29/09 at 3:47 AM, davidfrick2003 at yahoo.com (davef) 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

Because 4 x^3 is not equal to 4 (x^9)^(1/3) for all possible
values of x. In particular

In[26]:= FindInstance[4 (x^9)^(1/3) != 4 x^3, x]

Out[26]= {{x->8/5+2 I}}

If you want to get the result you expect you need to either tell
Mathematica x is a positive real or use PowerExpand. That is:

In[27]:= Assuming[x > 0, Simplify[4 (x^9)^(1/3)]]

Out[27]= 4 x^3

or

In[28]:= 4 (x^9)^(1/3) // PowerExpand

Out[28]= 4 x^3

Note you need to assume x is a positive real to get Simplify to
do what you want since,

In[29]:= 4 (x^9)^(1/3) /. x -> -1 // ComplexExpand

Out[29]= 2+2 I Sqrt[3]

```

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