$$\frac{0,{25}^{-2}·1,{75}^{-3}}{0,{75}^2·1,{25}^3}$$

$$=\frac{{\left({\displaystyle \frac{25}{100}}\right)}^{-2}·{\left(1{\displaystyle \frac{75}{100}}\right)}^{-3}}{{\left({\displaystyle \frac{75}{100}}\right)}^2·{\left(1{\displaystyle \frac{25}{100}}\right)}^3}$$

$$=\frac{{\left({\displaystyle \frac{1}{4}}\right)}^{-2}·{\left(1{\displaystyle \frac{3}{4}}\right)}^{-3}}{{\left({\displaystyle \frac{3}{4}}\right)}^2·{\left(1{\displaystyle \frac{1}{4}}\right)}^3}$$

$$=\frac{{\left({\displaystyle \frac{4}{1}}\right)}^2·{\left({\displaystyle \frac{7}{4}}\right)}^{-3}}{{\displaystyle \frac{9}{16}}·{\left({\displaystyle \frac{5}{4}}\right)}^3}$$

$$=\frac{{\displaystyle \frac{16}{1}}·{\left({\displaystyle \frac{4}{7}}\right)}^3}{{\displaystyle \frac{9}{16}}·{\left({\displaystyle \frac{5}{4}}\right)}^3}$$

$$=\frac{{\displaystyle \frac{16}{1}}·{\displaystyle \frac{64}{343}}}{{\displaystyle \frac{9}{16}}·{\displaystyle \frac{125}{64}}}$$

$$=\frac{{\displaystyle \frac{1024}{343}}}{{\displaystyle \frac{1125}{1024}}}$$

$$=\frac{1024·1024}{343·1125}$$

$$=\frac{1048576}{385875}$$