Question

rewrite using a single positive exponent.
$\frac{6^{-3}}{6^{5}}$

Explanation:

Step1: Apply exponent - subtraction rule

According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{6^{-3}}{6^{5}}$, we have $6^{-3-5}$.

Step2: Simplify the exponent

$-3 - 5=-8$, so we get $6^{-8}$.

Step3: Convert to positive exponent

Using the rule $a^{-n}=\frac{1}{a^{n}}$, $6^{-8}=\frac{1}{6^{8}}$.

Answer:

$\frac{1}{6^{8}}$