Question

which expression is equivalent to (10^2)^4?
1/10^4
1/10^(-8)
10^8
1/10^8

Explanation:

Step1: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^m)^n=a^{m\times n}$. Here $a = 10$, $m = 2$ and $n = 4$. So $(10^2)^4=10^{2\times4}$.

Step2: Calculate the exponent

$2\times4 = 8$, so $(10^2)^4=10^8$. None of the given options match $10^8$. If we assume there is a mistake in the problem and it was supposed to be $(10^{- 2})^4$, then by the power - of - a - power rule, $(10^{-2})^4=10^{-2\times4}=10^{-8}=\frac{1}{10^8}$.

Answer:

$\frac{1}{10^8}$ (assuming the original expression was $(10^{-2})^4$)