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

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

Evaluate

$$\frac{1}{16}=0.0625$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}$$

Factor

$$\frac{1}{2 ^ {4}} = 0.0625$$