razorback wrote:Here I recognize that a possible concept is a^2 - b^2 = (a+b)(a-b). When I plugged the exponents into that format I got 2^1, for answer A, but was wrong! GMATPrep offers no explanations to its problems.
If xy = 1, what is the value of 2^(x+y)^2 all over 2 ^(x-y)^2
A) 2
B) 4
C) 8
D) 16
E) 32
OA: D
Problem says, 2^(x+y)^2 all over 2 ^(x-y)^2
Therefore, 2^(x^2 + y^2 + 2xy) all over 2^(x^2 + y^2 - 2xy)
2^(x^2 + y^2 + 2 * 1) all over 2^(x^2 + y^2 - 2 * 1) (
because xy = 1)
2^(x^2 + y^2 + 2) all over 2^(x^2 + y^2 - 2)
2^(x^2 + y^2) * 2^2 all over 2^(x^2 + y^2) * 2^(-2)
(Expanding)
2^2 all over 2^(-2)
(2^(x^2 + y^2) got cancelled from numerator and denominator)
2^2 * 2^(2)
4 * 4
16
Hence, answer is
D
