Question

Question 39

In the following question, fill in the blanks to make the statements true.

The expression for $8^{-2}$ as a power with the base 2 is ___.

Answer 1

Given $8^{-2}$ where we can write $8=2\times 2\times 2$

$\therefore (8^{-2}=(2\times 2\times 2{)}^{-2}$
$=(2^3{)}^{-2}$
$=(2{)}^{3\times (-2)}=(2{)}^{-6}\left[\right(a^m{)}^n=a^{mn}]$

$Hence,8^{-2}=(2{)}^{-6}$