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

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

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

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

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