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

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

Calcular

$$\frac{16}{361}\approx 0.04432133$$

Pasos da solución

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

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

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

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

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

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

Calcula 2 á potencia de 1 e obtén 2.

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

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

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

Suma 2 e \frac{1}{9} para obter \frac{19}{9}.

$$\left(\frac{\frac{4}{9}}{\frac{19}{9}}\right)^{2}$$

Divide \frac{4}{9} entre \frac{19}{9} mediante a multiplicación de \frac{4}{9} polo recíproco de \frac{19}{9}.

$$\left(\frac{4}{9}\times \frac{9}{19}\right)^{2}$$

Multiplica \frac{4}{9} e \frac{9}{19} para obter \frac{4}{19}.

$$\left(\frac{4}{19}\right)^{2}$$

Calcula \frac{4}{19} á potencia de 2 e obtén \frac{16}{361}.

$$\frac{16}{361}$$

Factorizar

$$\frac{2 ^ {4}}{19 ^ {2}} = 0.0443213296398892$$