$$ \left(\frac{27}{64}\right)^{-\frac{2}{3}} $$

$$ =\left(\frac{64}{27}\right)^{\frac{2}{3}} $$

$$ =\left(\frac{(4)^{3}}{(3)^{3}}\right)^{\frac{2}{3}} $$

$$ =\left(\frac{(4)^{2}}{(3)^{2}}\right) $$

$$ =\frac{16}{9} $$