Question

Which expression is equivalent to 6-662?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

$\frac{6^{-6}}{6^2}$

STEP 2: Simplify the expression

$\begin{gathered} \frac{6^{-6}}{6^2} \\ \mathrm{Apply\: exponent\: rule}\colon\quad \frac{x^a}{x^b}=x^{a-b} \\ \frac{6^{-6}}{6^2}=6^{\mleft\{-6-2\mright\}} \\ \mathrm{Subtract\: the\: }indices\mathrm{\colon}\: -6-2=-8 \\ =6^{-8} \\ \mathrm{Apply\: exponent\: rule}\colon\quad \: a^{-b}=\frac{1}{a^b} \\ 6^{-8}=\frac{1}{6^8} \\ \frac{6^{-6}}{6^2}=\frac{1}{6^8} \end{gathered}$

Hence, the expression is equivalent to:

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