Solve 3/10+[(17/20-5/6-2/3):(-frac{3}{2}-5)^2+frac{8}{13}-frac{4}{5}]^3*[(frac{1}{7}+frac{3}{4}):(-frac{1}{2}+frac{3}{7})]

$$\frac { 3 } { 10 } + [ ( \frac { 17 } { 20 } - \frac { 5 } { 6 } - \frac { 2 } { 3 } ) : ( - \frac { 3 } { 2 } - 5 ) ^ { 2 } + \frac { 8 } { 13 } - \frac { 4 } { 5 } ] ^ { 3 } \cdot [ ( \frac { 1 } { 7 } + \frac { 3 } { 4 } ) : ( - \frac { 1 } { 2 } + \frac { 3 } { 7 } ) ]$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Subtract \frac{5}{6} from \frac{17}{20} to get \frac{1}{60}.

$$\frac{3}{10}+\left(\frac{\frac{1}{60}-\frac{2}{3}}{\left(-\frac{3}{2}-5\right)^{2}}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Subtract \frac{2}{3} from \frac{1}{60} to get -\frac{13}{20}.

$$\frac{3}{10}+\left(\frac{-\frac{13}{20}}{\left(-\frac{3}{2}-5\right)^{2}}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Subtract 5 from -\frac{3}{2} to get -\frac{13}{2}.

$$\frac{3}{10}+\left(\frac{-\frac{13}{20}}{\left(-\frac{13}{2}\right)^{2}}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Calculate -\frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$\frac{3}{10}+\left(\frac{-\frac{13}{20}}{\frac{169}{4}}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Divide -\frac{13}{20} by \frac{169}{4} by multiplying -\frac{13}{20} by the reciprocal of \frac{169}{4}.

$$\frac{3}{10}+\left(-\frac{13}{20}\times \frac{4}{169}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Multiply -\frac{13}{20} and \frac{4}{169} to get -\frac{1}{65}.

$$\frac{3}{10}+\left(-\frac{1}{65}+\frac{8}{13}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Add -\frac{1}{65} and \frac{8}{13} to get \frac{3}{5}.

$$\frac{3}{10}+\left(\frac{3}{5}-\frac{4}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Subtract \frac{4}{5} from \frac{3}{5} to get -\frac{1}{5}.

$$\frac{3}{10}+\left(-\frac{1}{5}\right)^{3}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Calculate -\frac{1}{5} to the power of 3 and get -\frac{1}{125}.

$$\frac{3}{10}-\frac{1}{125}\times \frac{\frac{1}{7}+\frac{3}{4}}{-\frac{1}{2}+\frac{3}{7}}$$

Add \frac{1}{7} and \frac{3}{4} to get \frac{25}{28}.

$$\frac{3}{10}-\frac{1}{125}\times \frac{\frac{25}{28}}{-\frac{1}{2}+\frac{3}{7}}$$

Add -\frac{1}{2} and \frac{3}{7} to get -\frac{1}{14}.

$$\frac{3}{10}-\frac{1}{125}\times \frac{\frac{25}{28}}{-\frac{1}{14}}$$

Divide \frac{25}{28} by -\frac{1}{14} by multiplying \frac{25}{28} by the reciprocal of -\frac{1}{14}.

$$\frac{3}{10}-\frac{1}{125}\times \frac{25}{28}\left(-14\right)$$

Multiply \frac{25}{28} and -14 to get -\frac{25}{2}.

$$\frac{3}{10}-\frac{1}{125}\left(-\frac{25}{2}\right)$$

Multiply -\frac{1}{125} and -\frac{25}{2} to get \frac{1}{10}.

$$\frac{3}{10}+\frac{1}{10}$$

Add \frac{3}{10} and \frac{1}{10} to get \frac{2}{5}.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$