Collecting Non-integer Exponents

However, when I try

it appears that Collect only works with integers. Is there a way to deal with this situation?

A: Daniel Lichtblau (danl@wolfram.com) answers: One way to perform the Collect is to allow a pattern variable for the exponent. This will in effect create a separate "variable" for each distinct power, and this suffices to do what you want in this particular example.