Question

which expression is equivalent to $\frac{4^{-8}}{4^{-4}}$? answer $\frac{1}{4^{12}}$ $4^{4}$ $\frac{1}{4^{4}}$ $\frac{1}{4^{2}}$

Explanation:

Step1: Apply exponent - subtraction rule

Use the rule $\frac{a^m}{a^n}=a^{m - n}$. Here $a = 4$, $m=-8$ and $n = - 4$. So $\frac{4^{-8}}{4^{-4}}=4^{-8-(-4)}$.

Step2: Simplify the exponent

Calculate $-8-(-4)=-8 + 4=-4$. So $4^{-8-(-4)}=4^{-4}$.

Step3: Convert negative - exponent to fraction

Use the rule $a^{-n}=\frac{1}{a^n}$. For $a = 4$ and $n = 4$, $4^{-4}=\frac{1}{4^4}$.

Answer:

$\frac{1}{4^4}$