Question

which expression is equivalent to $(10^{2})^{4}$? $\frac{1}{10^{8}}$, $\frac{1}{10^{- 8}}$, $10^{6}$, $\frac{1}{10^{6}}$

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 $(10^2)^4=10^{2\times4}=10^8$.

Step2: Analyze negative exponent rule

We know that $a^{-n}=\frac{1}{a^n}$. So $10^8=\frac{1}{10^{- 8}}$.

Answer:

$\frac{1}{10^{-8}}$