Solve sqrt[3]{27/8}-(2/5)^-1+4/3:(-8/9)-frac{2}{5}(-frac{10}{8})

$$\sqrt[ 3 ] { \frac { 27 } { 8 } } - ( \frac { 2 } { 5 } ) ^ { - 1 } + \frac { 4 } { 3 } : ( - \frac { 8 } { 9 } ) - \frac { 2 } { 5 } ( - \frac { 10 } { 8 } )$$

Evaluate

$$-2$$

Solution Steps

Calculate \sqrt[3]{\frac{27}{8}} and get \frac{3}{2}.

$$\frac{3}{2}-\left(\frac{2}{5}\right)^{-1}+\frac{\frac{4}{3}}{-\frac{8}{9}}-\frac{2}{5}\left(-\frac{10}{8}\right)$$

Calculate \frac{2}{5} to the power of -1 and get \frac{5}{2}.

$$\frac{3}{2}-\frac{5}{2}+\frac{\frac{4}{3}}{-\frac{8}{9}}-\frac{2}{5}\left(-\frac{10}{8}\right)$$

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

$$-1+\frac{\frac{4}{3}}{-\frac{8}{9}}-\frac{2}{5}\left(-\frac{10}{8}\right)$$

Divide \frac{4}{3} by -\frac{8}{9} by multiplying \frac{4}{3} by the reciprocal of -\frac{8}{9}.

$$-1+\frac{4}{3}\left(-\frac{9}{8}\right)-\frac{2}{5}\left(-\frac{10}{8}\right)$$

Multiply \frac{4}{3} and -\frac{9}{8} to get -\frac{3}{2}.

$$-1-\frac{3}{2}-\frac{2}{5}\left(-\frac{10}{8}\right)$$

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

$$-\frac{5}{2}-\frac{2}{5}\left(-\frac{10}{8}\right)$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{2}-\frac{2}{5}\left(-\frac{5}{4}\right)$$

Multiply \frac{2}{5} and -\frac{5}{4} to get -\frac{1}{2}.

$$-\frac{5}{2}-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$-\frac{5}{2}+\frac{1}{2}$$

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

$$-2$$

Factor

$$-2$$