It is worth mentioning that PowerExpand
assumes the variables are positive (real numbers). If the variable are not always positive, then the transformations made by PowerExpand
will be invalid.
PowerExpand
is more or less equivalent in this case:
Simplify[Sqrt[x^(9/2)], x > 0]
(* x^(9/4) *)
The second argument specified the assumption that x
is positive (and a real number). In this way, we specify exactly which variables are positive.
Another difference is that PowerExpand
expands powers and logarithms. Simplify
tries to contract the expression to an equivalent expression with the smallest expression tree. Expansion and contraction are sometimes in opposition to each other.