Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set - Page 353: 6

64

We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $(-\frac{1}{8})^{-2}=\frac{(-1)^{-2}}{8^{-2}}=\frac{1}{(-1)^{2}}\times8^{2}=\frac{1}{1}\times64=1\times64=64$.