Resolver (2/5^{2})^{2}(6^2/2^2*(2/3)^-1)^-2

$$( \frac { 2 } { 5 ^ { 2 } } ) ^ { 2 } ( \frac { 6 ^ { 2 } } { 2 ^ { 2 } } \cdot ( \frac { 2 } { 3 } ) ^ { - 1 } ) ^ { - 2 }$$

Calcular

$$\frac{16}{455625}\approx 0.000035117$$

Pasos da solución

Calcula 5 á potencia de 2 e obtén 25.

$$\left(\frac{2}{25}\right)^{2}\times \left(\frac{6^{2}}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Calcula \frac{2}{25} á potencia de 2 e obtén \frac{4}{625}.

$$\frac{4}{625}\times \left(\frac{6^{2}}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Calcula 6 á potencia de 2 e obtén 36.

$$\frac{4}{625}\times \left(\frac{36}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{4}{625}\times \left(\frac{36}{4}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Divide 36 entre 4 para obter 9.

$$\frac{4}{625}\times \left(9\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Calcula \frac{2}{3} á potencia de -1 e obtén \frac{3}{2}.

$$\frac{4}{625}\times \left(9\times \frac{3}{2}\right)^{-2}$$

Multiplica 9 e \frac{3}{2} para obter \frac{27}{2}.

$$\frac{4}{625}\times \left(\frac{27}{2}\right)^{-2}$$

Calcula \frac{27}{2} á potencia de -2 e obtén \frac{4}{729}.

$$\frac{4}{625}\times \frac{4}{729}$$

Multiplica \frac{4}{625} e \frac{4}{729} para obter \frac{16}{455625}.

$$\frac{16}{455625}$$

Factorizar

$$\frac{2 ^ {4}}{3 ^ {6} \cdot 5 ^ {4}} = 3.511659807956104 \times 10^{-5}$$