# simple(?) exponentiation simplification

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I'm beginning with sage. It sure looks great but I still have to understand what is the actual meaning of what I type in :-(

This is where I am currently stuck:

 
sage: simplify( (a/b)^c - (a^c)/(b^c) )
-a^c/b^c + (a/b)^c
 

I would have loved to get a nice clean $0$. What do I need to tell sage so that it sees that $(a/b)^c$ and $a^c/b^c$ are the same?

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It's a bit the same problem that here : http://ask.sagemath.org/question/2718/why-abssinpin-is-not-simplified-by-sinpin-when-n2 And the answer is a bit the same... "The most one can say here is that Maxima doesn't "know" that sin(pi/n) is, in fact, positive. The assumptions framework in Maxima (and hence Sage) is acknowledged to be fairly weak."

( 2013-07-11 15:50:21 +0200 )edit
1

? This is not the same thing. There isn't any particular reason that Sage (or any other system) should be asked to always expand such expressions; it could be arbitrarily computationally expensive to do so. Whereas when one *explicitly adds in an assumption*, it would be nice to have that happen (which is what the other question is about).

( 2013-07-11 16:01:06 +0200 )edit

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You can use the method .full_simplify():

sage: var('a b c')
(a, b, c)
sage: expression = (a/b)^c - (a^c)/(b^c)
sage: expression.full_simplify()
0

more