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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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