Let's start with
sage: x,p,q = var('x p q')
sage: ( exp(p*x - q*x)^(1/(p-q)) ).full_simplify()
e^x
So far so good. Let's bring an extra factor to the picture:
sage: ( (exp(p*x - q*x)/q)^(1/(p-q)) ).full_simplify()
(e^(p*x - q*x)/q)^(1/(p - q))
There is no simplification here. Why?
Also:
sage: ( (exp(p*x - q*x)/q)^(1/(p-q)) ).factor()
(e^(p*x - q*x)/q)^(1/(p - q))
does not produce the expected exp(x)*q^(-1/(p-q))
. How to get that result?