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]