$$\left(\frac{a^{-3}}{b^{-3}}\right)÷{\left(\frac{a^{-2}}{b^3}\right)}^{-2}$$

$$=\frac{b^3}{a^3}÷{\left(\frac{1}{a^2{b}^3}\right)}^{-2}$$

$$=\frac{b^3}{a^3}÷{\left(\frac{a^2·b^3}{1}\right)}^2$$

$$=\frac{b^3}{a^3}÷\frac{a^{2·2}·b^{3·2}}{1^2}$$

$$=\frac{b^3}{a^3}÷\frac{a^4·b^6}{1^2}$$

$$=\frac{\bcancel{b^3}}{a^3}·\frac{1}{a^4·\bcancel{b^6}}$$

$$=\frac{1}{a^{3+4}·b^3}$$