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

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

Evaluate

$$\frac{81}{16}=5.0625$$

Solution Steps

Cancel out \left(\frac{1}{3}\right)^{2} in both numerator and denominator.

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

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{\frac{1}{3}\times 27}{\frac{1}{2}\times 2^{3}}\right)^{2}$$

Multiply \frac{1}{3} and 27 to get 9.

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

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{9}{\frac{1}{2}\times 8}\right)^{2}$$

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

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

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$\frac{81}{16}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {4}} = 5\frac{1}{16} = 5.0625$$