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

$$1$$

Pasos da solución

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

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

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

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

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

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

Calcula 2 á potencia de 2 e obtén 4.

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

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

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

Multiplica 4 e \frac{1}{9} para obter \frac{4}{9}.

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

Divide \frac{4}{9} entre \frac{4}{9} para obter 1.

$$1^{2}$$

Calcula 1 á potencia de 2 e obtén 1.

$$1$$

Factorizar

$$1$$