Al efectuar las operaciones $\left ( \frac{3^{-2}\times 0.3\times 10}{2^{-3}\times 0.2\times 20} \right )^{2}$ el resultado es

$$\left ( \frac{3^{-2}\times 0.3\times 10}{2^{-3}\times 0.2\times 20} \right )^{2}$$

$$=\left ( \frac{\frac{1}{3^{2}}\times \frac{3}{10}\times 2\times 5}{\frac{1}{2^{3}}\times \frac{2}{10}\times 2^{2}\times 5} \right )^{2}$$

$$=\left ( \frac{\frac{2\times 3\times 5}{2\times 3^{2}\times 5}}{\frac{2^{3}\times 5}{2^{4}\times 5}} \right )^{2}$$

$$=\left ( \frac{\frac{1}{3}}{\frac{1}{2}} \right )^{2}$$

$$=\left ( \frac{2}{3} \right )^{2}$$

$$=\frac{4}{9}$$