Question

which expression is equivalent to $\frac{4^{-16}}{4^{-1}}$? $4^{-2}cdot4^{-8}$ $(4^{8})^{8}$ $4^{-15}$ $4^{15}$

Explanation:

Step1: Apply exponent - division rule

Use the rule $\frac{a^m}{a^n}=a^{m - n}$. For $\frac{4^{-16}}{4^{-1}}$, we have $a = 4$, $m=-16$, $n = - 1$. Then $4^{-16-(-1)}=4^{-16 + 1}=4^{-15}$.

Step2: Check other options

For $4^{-2}\cdot4^{-8}$, use the rule $a^m\cdot a^n=a^{m + n}$, so $4^{-2}\cdot4^{-8}=4^{-2-8}=4^{-10}$. For $(4^8)^8$, use the rule $(a^m)^n=a^{mn}$, so $(4^8)^8=4^{64}$. And $4^{15}$ is clearly not equal to $4^{-15}$.

Answer:

$4^{-15}$