Anonamy wrote:

Would someone please break down the steps to solve this question, step by step?

Hi,

the Q is

If \(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\), what is the value of xy?

(A) -1/4

(B) 1/2

(C) 0

(D) 1/4

(E) 1/2..

\(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\)

the power can be added if multiplied and can be subtracted if divided..

when you take a power to numerator from denominator, you have to just add - sign..

example 1/2^2=2^(-2)..

so \(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\) will become..

\(2^{(x+y)^2-(x-y)^2} = 2\)..

\(2^{(x^2+y^2+2xy-x^2-y^2+2xy)}=2\)..

so\(2^(4xy)=2^1\).

4xy=1 or xy=1/4..

D

Hope it is clear now..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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