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

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

Calcular

$$-2$$

Pasos da solución

Calcular \sqrt[3]{\frac{27}{8}} e obter \frac{3}{2}.

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

Calcula \frac{2}{5} á potencia de -1 e obtén \frac{5}{2}.

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

Resta \frac{5}{2} de \frac{3}{2} para obter -1.

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

Divide \frac{4}{3} entre -\frac{8}{9} mediante a multiplicación de \frac{4}{3} polo recíproco de -\frac{8}{9}.

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

Multiplica \frac{4}{3} e -\frac{9}{8} para obter -\frac{3}{2}.

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

Resta \frac{3}{2} de -1 para obter -\frac{5}{2}.

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

Reduce a fracción \frac{10}{8} a termos máis baixos extraendo e cancelando 2.

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

Multiplica \frac{2}{5} e -\frac{5}{4} para obter -\frac{1}{2}.

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

O contrario de -\frac{1}{2} é \frac{1}{2}.

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

Suma -\frac{5}{2} e \frac{1}{2} para obter -2.

$$-2$$

Factorizar

$$-2$$