64
Explanation:[tex]\text{Given: }\frac{1}{8^{-2}}[/tex][tex]\begin{gathered} \frac{1}{8^{-2}}\text{ = 1 }\div8^{-2} \\ In\text{ indices, for a}^{-b}\text{ = }\frac{1}{a^b} \\ \text{Applying the above to }8^{-2}\colon \\ 8^{-2}\text{ = }\frac{1}{8^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{8^{-2}}\text{ = 1 }\div\frac{1}{8^2} \\ \text{when dividing fractions, the second fraction is flipped} \\ \text{And the sign changes to multiplication:} \\ \text{1 }\div\frac{1}{8^2}\text{ = 1}\times\text{ }\frac{8^2}{1} \\ =\text{ 1 }\times\text{ 64 = 64} \\ \\ \frac{1}{8^{-2}}\text{ = 64} \end{gathered}[/tex]
