Art of Problem Solving: Fractional Exponent Problems Part 1

Art of Problem Solving's Richard Rusczyk tackles some problems involving fractional exponents.

[ilusion]

I do not understand how why can use exponent rules on fractional powers

[paysonbiker]

That was sort of helpful, but didn't address my particular problem:
2^(5/2) - 2^(3/2). Help?