I must have missed this somewhere, but factoring negative exponents? Help!

I just finished up trig in the spring and am taking a pre-cal summer course. We went over some algebraic review and came across a section that has me completely befuddled.

The homework has a few problems that say "factor the expression by removing the common factor with the smaller exponent". I have the answers for the following problems, but I don't have a full understanding of how to get to them.

First: x^5 - 2x^-2

Second: x^2 (x^2 +1)^-5 - (x^2 +1)^-4

Third: 2x^2 (x - 1)^1/2 - 5(x -1)^1/2

These are odd numbered problems in my text, so I do have the answers.. just not a clue how to really get to them. If anyone can help explain this, I would love you.

Edit: To be more specific, I do know that I am to factor out the smallest exponent. So for second problem I have:

(x^2 + 1)^-5 [x^2 -(x^2 + 1)] I'm just not sure where that ^-4 went.