Answer
$\dfrac{1}{16}$
Work Step by Step
Using $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{align*}
(-8)^{-4/3}
\\\\=
\dfrac{1}{(-8)^{4/3}}
\\\\=
\dfrac{1}{(\sqrt[3]{-8})^{4}}
\\\\=
\dfrac{1}{(-2)^{4}}
\\\\=
\dfrac{1}{16}
.\end{align*}