The question is:

Given X,Y,Z are uniformly distributed on (0,1), and are independant, prove that (XY)^Z is also uniform on (0,1)

I know the PDF of XY. My main question is, how do I work out the PDF of W^Z, where W has pdf -ln(t) and Z has pdf of 1? (Or, even better, how do I do it with general functions?).

Thanks for any help.