Tough algebra problem. Fractions and negative exponents
This problem with fractions and negative exponents is killing me.. I thought algebra was supposed to be easy, lol. ;) Any help greatly appreciated. I know the answer but cant get the steps right for some reason..
Simplify: Assume that all variables represent nonzero integers.
Here is the answer according to the book:
Ans. = 2^(-2a - 2b + ab)
I'm never able to get the final answer correct for some reason. I know it's hard to read these problems using computer text but I'd appreciate if you can bare with me and tell me where I'm messing up here.
Original Numerator: (2^-2)^a x (2^b)^-a
= 2^-2a x 2^-ba
= 1/(4^a) x 1/(2^ba)
= (1 / 8^2ab) <--simplified numerator
Original Denominator: (2^-2)^-b x (2^b)^-2a
= 2^2b x 2^-2ab
= 2^2b x 1/(2^ab)
= (2^2b / 2^ab) <--simplified denominator
So the new problem is:
(1 / 8^2ab) / (2^2b / 2^ab)
Every time I solve this with cross multiplication I get the wrong answer...so I'm guessing I messed up somewhere along the way.. Please heeelp!
I've tried everything I know but never seem to get the correct answer. I know typing formulas is a pain, but if someone could show me the steps involved I'd really appreciate it!