Answer
$\displaystyle \frac{27\sqrt{2}}{32}$
Work Step by Step
We simplify:
$(\displaystyle \frac{8}{9})^{-3/2}=(\frac{9}{8})^{3/2}=((\frac{9}{8})^{1/2})^3=(\sqrt{\frac{9}{8}})^{3}=(\frac{3}{2\sqrt{2}})^{3}
=\frac{3^{3}}{2^{3}(\sqrt{2})^{3}}=\frac{27}{8*2\sqrt{2}}=\frac{27}{16\sqrt{2}}
=\frac{27}{16\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{27\sqrt{2}}{16*2}=\frac{27\sqrt{2}}{32}$
