Answer
$\dfrac{5}{2}$
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:
$=\dfrac{1}{(\frac{8}{125})^{\frac{1}{3}}}
\\=\dfrac{1}{\sqrt[3]{\dfrac{8}{125}}}
\\=\dfrac{1}{\sqrt[3]{\left(\dfrac{2}{5}\right)^3}}
\\=\dfrac{1}{\frac{2}{5}}
\\=1 \cdot \dfrac{5}{2}
\\=\dfrac{5}{2}$
