Solve [frac{2^{2}*(1/2)^3}{3^2(2/3)^2}]^2=

$$[ \frac { 2 ^ { 2 } \times ( \frac { 1 } { 2 } ) ^ { 3 } } { 3 ^ { 2 } ( \frac { 2 } { 3 } ) ^ { 2 } } ] ^ { 2 } =$$

Evaluate

$$\frac{1}{64}=0.015625$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\left(\frac{4\times \frac{1}{8}}{3^{2}\times \left(\frac{2}{3}\right)^{2}}\right)^{2}$$

Multiply 4 and \frac{1}{8} to get \frac{1}{2}.

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

Express \frac{\frac{1}{2}}{4} as a single fraction.

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

Multiply 2 and 4 to get 8.

$$\left(\frac{1}{8}\right)^{2}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$\frac{1}{64}$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$