Solve (1/5-3/5-1/2)(1-frac{5/6)^-2}{sqrt[3]{-3(-frac{1}{3})^-2}*frac{2}{3}*6}

$$\frac { ( \frac { 1 } { 5 } - \frac { 3 } { 5 } - \frac { 1 } { 2 } ) ( 1 - \frac { 5 } { 6 } ) ^ { - 2 } } { \sqrt[ 3 ] { - 3 ( - \frac { 1 } { 3 } ) ^ { - 2 } } \times \frac { 2 } { 3 } \times 6 }$$

Evaluate

$$\frac{27}{10}=2.7$$

Solution Steps

Subtract \frac{3}{5} from \frac{1}{5} to get -\frac{2}{5}.

$$\frac{\left(-\frac{2}{5}-\frac{1}{2}\right)\left(1-\frac{5}{6}\right)^{-2}}{\sqrt[3]{-3\left(-\frac{1}{3}\right)^{-2}}\times \frac{2}{3}\times 6}$$

Subtract \frac{1}{2} from -\frac{2}{5} to get -\frac{9}{10}.

$$\frac{-\frac{9}{10}\left(1-\frac{5}{6}\right)^{-2}}{\sqrt[3]{-3\left(-\frac{1}{3}\right)^{-2}}\times \frac{2}{3}\times 6}$$

Subtract \frac{5}{6} from 1 to get \frac{1}{6}.

$$\frac{-\frac{9}{10}\times \left(\frac{1}{6}\right)^{-2}}{\sqrt[3]{-3\left(-\frac{1}{3}\right)^{-2}}\times \frac{2}{3}\times 6}$$

Calculate \frac{1}{6} to the power of -2 and get 36.

$$\frac{-\frac{9}{10}\times 36}{\sqrt[3]{-3\left(-\frac{1}{3}\right)^{-2}}\times \frac{2}{3}\times 6}$$

Multiply -\frac{9}{10} and 36 to get -\frac{162}{5}.

$$\frac{-\frac{162}{5}}{\sqrt[3]{-3\left(-\frac{1}{3}\right)^{-2}}\times \frac{2}{3}\times 6}$$

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

$$\frac{-\frac{162}{5}}{\sqrt[3]{-3\times 9}\times \frac{2}{3}\times 6}$$

Multiply -3 and 9 to get -27.

$$\frac{-\frac{162}{5}}{\sqrt[3]{-27}\times \frac{2}{3}\times 6}$$

Calculate \sqrt[3]{-27} and get -3.

$$\frac{-\frac{162}{5}}{-3\times \frac{2}{3}\times 6}$$

Multiply -3 and \frac{2}{3} to get -2.

$$\frac{-\frac{162}{5}}{-2\times 6}$$

Multiply -2 and 6 to get -12.

$$\frac{-\frac{162}{5}}{-12}$$

Express \frac{-\frac{162}{5}}{-12} as a single fraction.

$$\frac{-162}{5\left(-12\right)}$$

Multiply 5 and -12 to get -60.

$$\frac{-162}{-60}$$

Reduce the fraction \frac{-162}{-60} to lowest terms by extracting and canceling out -6.

$$\frac{27}{10}$$

Factor

$$\frac{3 ^ {3}}{2 \cdot 5} = 2\frac{7}{10} = 2.7$$