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

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

Evaluate

$$4$$

Solution Steps

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

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

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

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

Multiply \frac{16}{81} and \frac{9}{4} to get \frac{4}{9}.

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

Calculate 2 to the power of 1 and get 2.

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

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

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

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

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

Divide \frac{4}{9} by \frac{2}{9} by multiplying \frac{4}{9} by the reciprocal of \frac{2}{9}.

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

Multiply \frac{4}{9} and \frac{9}{2} to get 2.

$$2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4$$

Factor

$$2^{2}$$