Answer
$\dfrac{1}{4}$
Work Step by Step
RECALL:
(i) $a^{-\frac{m}{n}}=\dfrac{1}{a^{\frac{m}{n}}}$
(ii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Use the rules above to obtain:
$=\dfrac{1}{(-8)^{\frac{2}{3}}}
\\=\dfrac{1}{\sqrt[3]{(-8)^2}}
\\=\dfrac{1}{\sqrt[3]{64}}
\\=\dfrac{1}{\sqrt[3]{4^3}}
\\=\dfrac{1}{4}$
