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

$$4$$

Pasos da solución

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

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

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

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

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

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

Calcula 2 á potencia de 1 e obtén 2.

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

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

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

Multiplica 2 e \frac{1}{9} para obter \frac{2}{9}.

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

Divide \frac{4}{9} entre \frac{2}{9} mediante a multiplicación de \frac{4}{9} polo recíproco de \frac{2}{9}.

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

Multiplica \frac{4}{9} e \frac{9}{2} para obter 2.

$$2^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$4$$

Factorizar

$$2^{2}$$