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

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

Evaluate

$$1$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Multiply 4 and \frac{1}{9} to get \frac{4}{9}.

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

Divide \frac{4}{9} by \frac{4}{9} to get 1.

$$1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1$$

Factor

$$1$$