Which of the following is equivalent to (10^2)^n+1 ?

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GMAT Panda · Accepted Answer

A We apply the exponent-of-a-power rule to simplify the nested exponent. (10^2)^n+1 = 10^2(n+1) We distribute the exponent multiplication inside the parentheses. 2(n+1) = 2n + 2 We use the property of multiplying exponents with the same base to split the result into a product. 10^2n+2 = 10^2 10^2n

Explanation	Calculations	Help
$We apply the exponent-of-a-power rule to simplify the nested exponent.$	$(1 0^{2})^{n + 1} = 1 0^{2 (n + 1)}$
$We distribute the exponent multiplication inside the parentheses.$	$2 (n + 1) = 2 n + 2$
$We use the property of multiplying exponents with the same base to split the result into a product.$	$1 0^{2 n + 2} = 1 0^{2} \times 1 0^{2 n}$

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