If n is a positive integer, then (-2^n)^-2+(2^-n)^2=

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GMAT Panda · Accepted Answer

2^-2n + 1 We simplify the first term by separating the factor -1 and applying the rule for multiplying negative numbers an even number of times. (-2^n)^-2 = (-1)^-2 2^-2n = 1 2^-2n = 2^-2n We simplify the second term by applying the power-of-a-power rule to the exponent. (2^-n)^2 = 2^-2n We add the two identical simplified terms to find the final expression. 2^-2n + 2^-2n = 2 2^-2n = 2^-2n + 1

Explanation	Calculations	Help
$We simplify the first term by separating the factor - 1 and applying the rule for multiplying negative numbers an even number of times.$	$(- 2^{n})^{- 2} = (- 1)^{- 2} \times 2^{- 2 n} = 1 \times 2^{- 2 n} = 2^{- 2 n}$
$We simplify the second term by applying the power-of-a-power rule to the exponent.$	$(2^{- n})^{2} = 2^{- 2 n}$
$We add the two identical simplified terms to find the final expression.$	$2^{- 2 n} + 2^{- 2 n} = 2 \times 2^{- 2 n} = 2^{- 2 n + 1}$

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