#### Answer

$\dfrac{1}{2}$

#### Work Step by Step

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}