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 ___.

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Solution

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

$∴ (8^{- 2} = (2 \times 2 \times 2)^{- 2}$
$= (2^{3})^{- 2}$
$= (2)^{3 \times (- 2)} = (2)^{- 6} [(a^{m})^{n} = a^{m n}]$

$H e n c e, 8^{- 2} = (2)^{- 6}$

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