repost from another person's question: application

[wignewton]

Someone posted this question about 2 weeks ago.
"I don’t understand how does a^b(1 - a^-1) becomes a^b-1(a - 1), and how does p(q + r) + s(q + r) becomes (p + s)(q + r)? Please also provide where is this explained in the guides."

I am curious about the first question: a^b(1 - a^-1) becomes a^b-1(a - 1)
I understand the logic behind how you arrive at the answer. However, I have not seen a gmat practice question inside the OG or anywhere else that this is applicable.
When do we know that we need to use this method. The reason I ask is that, like the first poster, this is difficult for me to compute as is, much less know when to pull this method out of the toolbox! Thanks!

[StaceyKoprince]

It's pretty rare that we would need to pull a negative exponent out of something in parentheses. The only reason I can think of is when we want the stuff inside the parentheses to match something inside another set of parentheses (eg, to cancel out on the top and bottom of a fraction).

You'd know to do this if you have two terms inside parentheses that could almost cancel out, but they're not quite in the same form. So you'd ask yourself how you could get them into the same form so you could cancel them out... and one of the ways you might do that is above.