<s>[INST] Math question from the GMATprep If $xy=1$ what is the value of: $2^{(x+y)^2}/2^{(x-y)^2}$
A 1
B 2
C 4
D 16
E 19

$(x+y)^2/(x-y)^2$ because $2$ just cancels out from numerator and denominator, right?
 [/INST] Using exponentiation rules, it can be simplified.
$$ \frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2^{(x+y)^² - (x-y)^2} = 2^{x^2 + 2xy + y^2 - (x^2 - 2xy + y^2)} = 2^{4xy} = \left(2^{4}\right)^{xy} = 16 $$
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