Comment #1 on issue 2008 by smichr: Inconsistencies for Pow**n and exp***n
http://code.google.com/p/sympy/issues/detail?id=2008

FWIW, if it's version 2, that makes looking for polynomial type expressions easier since the integer part is split out of the "base". If you put an assumption on x they behave the same, but you can always pull the integer in or out of the exponent regardless of the base, so it seems like that should be done regardless of the assumptions on the base:

var('x')
x
(2**x)**2
(2**x)**2
powsimp(_)
(2**x)**2
var('x', positive=1)
x
(2**x)**2
2**(2*x)
powsimp(_)
4**x


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