PowerExpand[expr] expands all powers of products and powers.
Example: PowerExpand[Sqrt[x y]] .
PowerExpand converts (a b)^c to a^c b^c, whatever the form of c is.
PowerExpand also converts (a^b)^c to a^(b c), whatever the form of c is.
The transformations made by PowerExpand are correct in general only if c is an integer or a and b are positive real numbers.
PowerExpand converts Log[a^b] to b Log[a].
See The Mathematica Book: Section 1.4.5 and Section 3.3.1.
See also: Expand, Distribute, ComplexExpand, FullSimplify.