Resolver ((frac{2/3)^{4}(3/2)^2}{2^2+(1/3)^2})^2=

$$( \frac { ( \frac { 2 } { 3 } ) ^ { 4 } ( \frac { 3 } { 2 } ) ^ { 2 } } { 2 ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 2 } } ) ^ { 2 } =$$

Calcular

$$\frac{16}{1369}\approx 0.011687363$$

Pasos da solución

Calcula \frac{2}{3} á potencia de 4 e obtén \frac{16}{81}.

$$\left(\frac{\frac{16}{81}\times \left(\frac{3}{2}\right)^{2}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Calcula \frac{3}{2} á potencia de 2 e obtén \frac{9}{4}.

$$\left(\frac{\frac{16}{81}\times \frac{9}{4}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Multiplica \frac{16}{81} e \frac{9}{4} para obter \frac{4}{9}.

$$\left(\frac{\frac{4}{9}}{2^{2}+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\left(\frac{\frac{4}{9}}{4+\left(\frac{1}{3}\right)^{2}}\right)^{2}$$

Calcula \frac{1}{3} á potencia de 2 e obtén \frac{1}{9}.

$$\left(\frac{\frac{4}{9}}{4+\frac{1}{9}}\right)^{2}$$

Suma 4 e \frac{1}{9} para obter \frac{37}{9}.

$$\left(\frac{\frac{4}{9}}{\frac{37}{9}}\right)^{2}$$

Divide \frac{4}{9} entre \frac{37}{9} mediante a multiplicación de \frac{4}{9} polo recíproco de \frac{37}{9}.

$$\left(\frac{4}{9}\times \frac{9}{37}\right)^{2}$$

Multiplica \frac{4}{9} e \frac{9}{37} para obter \frac{4}{37}.

$$\left(\frac{4}{37}\right)^{2}$$

Calcula \frac{4}{37} á potencia de 2 e obtén \frac{16}{1369}.

$$\frac{16}{1369}$$

Factorizar

$$\frac{2 ^ {4}}{37 ^ {2}} = 0.01168736303871439$$