Re: FullSimplify doesn't simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg32778] Re: FullSimplify doesn't simplify*From*: "John Doty" <jpd at w-d.org>*Date*: Sat, 9 Feb 2002 05:11:54 -0500 (EST)*References*: <a404nb$bqk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <a404nb$bqk$1 at smc.vnet.net>, "Ken Morgan" <kmorga51 at calvin.edu> wrote: > 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? Sure: In[1]:= (x y)^n == (x^n)(y^n)/.{x->-1,y->-1,n->1/2} Out[1]= False It's true in some common special cases: In[2]:= FullSimplify[(x y)^n == (x^n)(y^n), Element[n,Integers]] Out[2]= True In[3]:= FullSimplify[(x y)^n == (x^n)(y^n), X>=0 && y>=0] Out[3]= True If you like living dangerously you can use PowerExpand: In[4]:= PowerExpand[(x y)^n == (x^n)(y^n)] Out[4]= True Beware, however, that PowerExpand's transformations are not valid in general. -- | John Doty "You can't confuse me, that's my job." | Home: jpd at w-d.org | Work: jpd at space.mit.edu