$$\left({\left(\frac{3x^{-3}}{5y^{-2}}\right)}^{-3}÷{\left(\frac{9x^{-2}}{5y^{-3}}\right)}^{-2}\right)·\frac{x^{-6}y}{15}$$

$$=\left({\left(\frac{3y^2}{5x^3}\right)}^{-3}÷{\left(\frac{9y^3}{5x^2}\right)}^{-2}\right)·\frac{y}{15x^6}$$

$$=\left({\left(\frac{5x^3}{3y^2}\right)}^3÷{\left(\frac{5x^2}{9y^3}\right)}^2\right)·\frac{y}{15x^6}$$

$$=\left(\frac{5^3{x}^{3·3}}{3^3{y}^{2·3}}÷\frac{5^2{x}^{2·2}}{9^2{y}^{3·2}}\right)·\frac{y}{15x^6}$$

$$=\left(\frac{125x^9}{27y^6}÷\frac{25x^4}{81y^6}\right)·\frac{y}{15x^6}$$

$$=\left(\frac{\bcancel{125 }\bcancel{x^9}}{\cancel{27} \cancel{y^6}}·\frac{\cancel{81} \cancel{y^6}}{\bcancel{25 }\bcancel{x^4}}\right)·\frac{y}{15x^6}$$

$$=\frac{\bcancel{15x^5}·}{1}·\frac{y}{\bcancel{15x^6}}$$