Question

1. simplify \\(\frac{6^{-3}}{6^{5}}\\). (4 points) \\(\bigcirc\\) \\(6^{8}\\) \\(\bigcirc\\) \\(\frac{1}{6^{2}}\\) \\(\bigcirc\\) \\(\frac{1}{6^{8}}\\) \\(\bigcirc\\) \\(6^{-2}\\)

Explanation:

Step1: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $a^m / a^n = a^{m-n}$.
$\frac{6^{-3}}{6^{5}} = 6^{-3-5}$

Step2: Calculate the exponent

Compute the value of the exponent.
$6^{-3-5} = 6^{-8}$

Step3: Rewrite positive exponent form

A negative exponent means reciprocal: $a^{-k} = \frac{1}{a^k}$.
$6^{-8} = \frac{1}{6^{8}}$

Answer:

$\frac{1}{6^{8}}$ (Option C)