Question

Which expression is equivalent to 6-662?

Answer 1

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

STEP 1: Write the given expression

`(6^(-6))/(6^2)`

STEP 2: Simplify the expression

`\begin{gathered} (6^(-6))/(6^2) \\ \mathrm{Apply\: exponent\: rule}\colon\quad (x^a)/(x^b)=x^(a-b) \\ (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)=(1)/(a^b) \\ 6^(-8)=(1)/(6^8) \\ (6^(-6))/(6^2)=(1)/(6^8) \end{gathered}`

Hence, the expression is equivalent to:

`(1)/(6^8)`