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simplifying/factoring fractions to fractional powers

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?

simplifying/factoring fractions to fractional powers

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?