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*}
(-64)^{-2/3}
\\\\=
\dfrac{1}{(-64)^{2/3}}
\\\\=
\dfrac{1}{(\sqrt[3]{-64})^{2}}
\\\\=
\dfrac{1}{(-4)^{2}}
\\\\=
\dfrac{1}{16}
.\end{align*}