Simplify the following:

$(64)^{-\dfrac{2}{3}} ÷ (9)^{-\dfrac{3}{2}}$

Given,

$\Rightarrow (64)^{-\dfrac{2}{3}} ÷ (9)^{-\dfrac{3}{2}} = \Big(\dfrac{1}{64}\Big)^{\dfrac{2}{3}} ÷ \Big(\dfrac{1}{9}\Big)^{\dfrac{3}{2}} \\[1em] = \Big(\dfrac{1}{2^6}\Big)^{\dfrac{2}{3}} ÷ \Big(\dfrac{1}{3^2}\Big)^{\dfrac{3}{2}} \\[1em] = \dfrac{(1)^{\dfrac{2}{3}}}{2^{6 \times \dfrac{2}{3}}} ÷ \dfrac{(1)^{\dfrac{3}{2}}}{3^{2 \times \dfrac{3}{2}}} \\[1em] = \dfrac{1}{2^4} ÷ \dfrac{1}{3^3} \\[1em] = \dfrac{1}{2^4} \times 3^3 \\[1em] = \dfrac{27}{16} = 1\dfrac{11}{16}.$

Hence, $(64)^{-\dfrac{2}{3}} ÷ (9)^{-\dfrac{3}{2}} = 1\dfrac{11}{16}$.