If xy = 1, what is the value of (2^((x+y)^2))/(2^((x-y)^2))?

16 (D). We apply exponent subtraction to combine the powers of two.

GMAT Arithmetic: If xy = 1, what is the value…

If x y = 1, what is the value of \frac{2 ^{(x + y)^{2}}}{2 ^{(x - y)^{2}}} ?

development formulascalculations

Explanation	Calculations	Help
$We apply exponent subtraction to combine the powers of two.$	$\frac{2 ^{(x + y)^{2}}}{2 ^{(x - y)^{2}}} = 2^{(x + y)^{2} - (x - y)^{2}}$
$We apply "Development Formulas - Squares of +/-" to expand each squared binomial.$	$(x + y)^{2} = x^{2} + y^{2} + 2 x y (x - y)^{2} = x^{2} + y^{2} - 2 x y$
$We subtract the expanded exponents to simplify the exponent expression.$	$(x + y)^{2} - (x - y)^{2} = 4 x y$
$We substitute the given value into the exponent and evaluate the power of two.$	$2^{4 x y} = 2^{4 \times 1} = 2^{4} = 16$

16 (D)