Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 53

$\dfrac{1}{2}$

Using the laws of exponents, the given expression, $ 8^{-1/3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{8^{1/3}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ \dfrac{1}{8^{1/3}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{\sqrt[3]{8}} \\\\= \dfrac{1}{\sqrt[3]{(2)^3}} \\\\= \dfrac{1}{2} .\end{array}