When letting Mathematica simplify
(a^(-5) b (a^2 c^3)^3)/((a b^2 )^(-2) c^7)
it returns the 'correct' answer
a^3 b^5 c^2
But, when entering
((a^5 b)^(1/2) c^3)/(a^5 (b^4 c^5)^(1/4))
the return is far from as 'correct' as the above. (Can it be the 1/2 and 1/4?)
How can I get Mathematica to always return an answer with
a^(...) b^(...) c^(...)
even if that means (negative) fractions in (...)? And, can negative exponentials be ruled out so that Mathematica responds with a fraction with expressions in numerator and denominator with only positive exponentials? TIA