Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 223: 10

$-8$

Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$ and the laws of exponents, the given expression, $ \left( -\dfrac{1}{2} \right)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{-1}{2} \right)^{-3} \\\\= \dfrac{(-1)^{-3}}{2^{-3}} \\\\= \dfrac{2^{3}}{(-1)^{3}} \\\\= \dfrac{8}{-1} \\\\= -8 .\end{array}