Question

How do you simplify $4^{-2}$?

Answer 1

Use the concept of negative exponent and inverse:

$4^{-2}$can be written as $\frac{1}{4^2}$.

Now, simplify $4^2$ as shown:

$$\begin{gathered} 4^2=4\times 4 \\ =16 \end{gathered}$$

Take reciprocal on both sides:

$$\begin{gathered} \frac{1}{4^2}=\frac{1}{16} \\ \Rightarrow 4^{-2}=\frac{1}{16} \end{gathered}$$

Hence, $4^{-2}=\frac{1}{16}$.