2^{(x+y)^2} / 2^{(x-y)^2} = 2
=>(x+y)^2 - (x-y)^2 = 1
=> 4xy = 1
xy=1/4

Ans D
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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..
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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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On solving
2^4xy = 2^1
4xy = 1
xy = 1/4
D
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