$$A=\frac{1^{-1}+2^{-2}}{{\left({\displaystyle \frac{2}{3}}\right)}^{-2}+4^{-1}·5+0,5^{-2}}$$

$$A=\frac{{\displaystyle \frac{1}{1^1}}+{\displaystyle \frac{1}{2^2}}}{{\left({\displaystyle \frac{3}{2}}\right)}^2+{\displaystyle \frac{1}{4^1}}·5+{\left({\displaystyle \frac{5}{10}}\right)}^{-2}}$$

$$A=\frac{{\displaystyle \frac{1}{1}}+{\displaystyle \frac{1}{4}}}{{\displaystyle \frac{9}{4}}+{\displaystyle \frac{1}{4}}·5+{\left({\displaystyle \frac{1}{2}}\right)}^{-2}}$$

$$A=\frac{{\displaystyle \frac{4}{4}}+{\displaystyle \frac{1}{4}}}{{\displaystyle \frac{9}{4}}+{\displaystyle \frac{5}{4}}+{\left({\displaystyle \frac{2}{1}}\right)}^2}$$

$$A=\frac{{\displaystyle \frac{5}{4}}}{{\displaystyle \frac{14}{4}}+{\displaystyle \frac{4}{1}}}$$

$$A=\frac{{\displaystyle \frac{5}{4}}}{{\displaystyle \frac{14}{4}}+{\displaystyle \frac{16}{4}}}$$

$$A=\frac{{\displaystyle \frac{5}{4}}}{{\displaystyle \frac{30}{4}}}$$

$$A=\frac{5·\cancel{4}}{\cancel{4}·30}$$

$$A=\frac{5}{30}$$