$${\left(\frac{y^{-2}}{x^{-2}}\right)}^{-3}÷{\left(\frac{x^{-1}}{y^2}\right)}^{-3}$$

$$={\left(\frac{x^2}{y^2}\right)}^{-3}÷{\left(\frac{1}{y^2·x^1}\right)}^{-3}$$

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

$$=\frac{y^{2·3}}{x^{2·3}}÷\frac{y^{2·3}·x^3}{1}$$

$$=\frac{y^6}{x^6}÷\frac{y^6·x^3}{1}$$

$$=\frac{\bcancel{y^6}}{x^6}·\frac{1}{\bcancel{y^6}·x^3}$$

$$=\frac{1}{x^{6+3}}$$