Answer
$\frac{9}{4}$
Work Step by Step
$(\frac{8}{27})^{-\frac{2}{3}}=\frac{1}{(\frac{8}{27})^{\frac{2}{3}}}=\frac{1}{\sqrt[3] ((\frac{8}{27})^{2})}=\frac{1}{\sqrt[3] (\frac{64}{27\times27})}=\frac{1}{\frac{4}{3\times3}}=\frac{1}{\frac{4}{9}}=\frac{9}{4}$
We know that $\sqrt[3] 64=4$, because $4^{3}=64$.
We know that $\sqrt[3] 27=3$, because $3^{3}=27$.
