Question

The expression for$8^{-2}$ as a power with the base $2$ is _________. Fill in the blank to make the statement true.

Answer 1

The expression is $8^{-2}$

$$\begin{gathered} \therefore 8^{-2}={\left(2\times 2\times 2\right)}^{-2} \\ ={\left(2^3\right)}^{-2} \end{gathered}$$

By using the law of exponent ${\left(a^m\right)}^n=a^{mn}$

$$\begin{gathered} =2^{\left(3\times \left(-2\right)\right)} \\ =2^{\left(-6\right)} \end{gathered}$$

Hence, The expression for$8^{-2}$ as a power with the base $2$ is $\underline{\mathbf{-}\mathbf{}\mathbf{6}}$