Solve sqrt{[(2/3)^2:4/3+(2/5+3/2-frac{6}{10})*frac{10}{13}]:frac{4}{3^3}}=

$$\sqrt { [ ( \frac { 2 } { 3 } ) ^ { 2 } : \frac { 4 } { 3 } + ( \frac { 2 } { 5 } + \frac { 3 } { 2 } - \frac { 6 } { 10 } ) \cdot \frac { 10 } { 13 } ] : \frac { 4 } { 3 ^ { 3 } } } =$$

Evaluate

$$3$$

Solution Steps

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

$$\sqrt{\frac{\frac{\frac{4}{9}}{\frac{4}{3}}+\left(\frac{2}{5}+\frac{3}{2}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Divide \frac{4}{9} by \frac{4}{3} by multiplying \frac{4}{9} by the reciprocal of \frac{4}{3}.

$$\sqrt{\frac{\frac{4}{9}\times \frac{3}{4}+\left(\frac{2}{5}+\frac{3}{2}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Multiply \frac{4}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{4\times 3}{9\times 4}+\left(\frac{2}{5}+\frac{3}{2}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Cancel out 4 in both numerator and denominator.

$$\sqrt{\frac{\frac{3}{9}+\left(\frac{2}{5}+\frac{3}{2}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{\frac{1}{3}+\left(\frac{2}{5}+\frac{3}{2}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{3}{2} to fractions with denominator 10.

$$\sqrt{\frac{\frac{1}{3}+\left(\frac{4}{10}+\frac{15}{10}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Since \frac{4}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{1}{3}+\left(\frac{4+15}{10}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Add 4 and 15 to get 19.

$$\sqrt{\frac{\frac{1}{3}+\left(\frac{19}{10}-\frac{6}{10}\right)\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Since \frac{19}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{1}{3}+\frac{19-6}{10}\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Subtract 6 from 19 to get 13.

$$\sqrt{\frac{\frac{1}{3}+\frac{13}{10}\times \frac{10}{13}}{\frac{4}{3^{3}}}}$$

Cancel out \frac{13}{10} and its reciprocal \frac{10}{13}.

$$\sqrt{\frac{\frac{1}{3}+1}{\frac{4}{3^{3}}}}$$

Convert 1 to fraction \frac{3}{3}.

$$\sqrt{\frac{\frac{1}{3}+\frac{3}{3}}{\frac{4}{3^{3}}}}$$

Since \frac{1}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{1+3}{3}}{\frac{4}{3^{3}}}}$$

Add 1 and 3 to get 4.

$$\sqrt{\frac{\frac{4}{3}}{\frac{4}{3^{3}}}}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{\frac{\frac{4}{3}}{\frac{4}{27}}}$$

Divide \frac{4}{3} by \frac{4}{27} by multiplying \frac{4}{3} by the reciprocal of \frac{4}{27}.

$$\sqrt{\frac{4}{3}\times \frac{27}{4}}$$

Multiply \frac{4}{3} times \frac{27}{4} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{4\times 27}{3\times 4}}$$

Cancel out 4 in both numerator and denominator.

$$\sqrt{\frac{27}{3}}$$

Divide 27 by 3 to get 9.

$$\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$3$$

Factor

$$3$$