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

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

Evaluate

$$81$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 4 and get 81.

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

Multiply \frac{1}{9} and 81 to get 9.

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

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

$$\left(\frac{9}{\frac{1}{8}\times 2^{3}}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

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

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

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

Anything divided by one gives itself.

$$9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$81$$

Factor

$$3^{4}$$