Question

rewrite $8^{-4}$ using a positive exponent.
$8^{-4}=\frac{1}{8}\cdot\frac{1}{8}\cdot\frac{1}{8}\cdot\frac{1}{8}$
$= ?$
$8^{1}=8$
$8^{0}=1$
$8^{-1}=\frac{1}{8}$
$8^{-2}=\frac{1}{8}\cdot\frac{1}{8}$
$8^{-3}=\frac{1}{8}\cdot\frac{1}{8}$

Explanation:

Step1: Recall negative exponent rule

For any non-zero $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$

Step2: Apply rule to $8^{-4}$

$8^{-4} = \frac{1}{8^4}$

Step3: Verify with given product

$\frac{1}{8} \cdot \frac{1}{8} \cdot \frac{1}{8} \cdot \frac{1}{8} = \frac{1}{8^4}$

Answer:

$\frac{1}{8^4}$