Answer
$\dfrac{3}{2}$
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:
$=\dfrac{1}{(\frac{8}{27})^{\frac{1}{3}}}
\\=\dfrac{1}{\sqrt[3]{\dfrac{8}{27}}}
\\=\dfrac{1}{\sqrt[3]{\left(\dfrac{2}{3}\right)^3}}
\\=\dfrac{1}{\frac{2}{3}}
\\=1 \cdot \dfrac{3}{2}
\\=\dfrac{3}{2}$
