Resolver (1-5/3)^-2/frac{1{2}+5/4}*frac{4/5*frac{15}{2}}{(frac{1}{2})^-3}

$$\frac { ( 1 - \frac { 5 } { 3 } ) ^ { - 2 } } { \frac { 1 } { 2 } + \frac { 5 } { 4 } } \cdot \frac { \frac { 4 } { 5 } \cdot \frac { 15 } { 2 } } { ( \frac { 1 } { 2 } ) ^ { - 3 } }$$

Calcular

$$\frac{27}{28}\approx 0.964285714$$

Pasos da solución

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

$$\frac{\left(-\frac{2}{3}\right)^{-2}}{\frac{1}{2}+\frac{5}{4}}\times \frac{\frac{4}{5}\times \frac{15}{2}}{\left(\frac{1}{2}\right)^{-3}}$$

Calcula -\frac{2}{3} á potencia de -2 e obtén \frac{9}{4}.

$$\frac{\frac{9}{4}}{\frac{1}{2}+\frac{5}{4}}\times \frac{\frac{4}{5}\times \frac{15}{2}}{\left(\frac{1}{2}\right)^{-3}}$$

Suma \frac{1}{2} e \frac{5}{4} para obter \frac{7}{4}.

$$\frac{\frac{9}{4}}{\frac{7}{4}}\times \frac{\frac{4}{5}\times \frac{15}{2}}{\left(\frac{1}{2}\right)^{-3}}$$

Divide \frac{9}{4} entre \frac{7}{4} mediante a multiplicación de \frac{9}{4} polo recíproco de \frac{7}{4}.

$$\frac{9}{4}\times \frac{4}{7}\times \frac{\frac{4}{5}\times \frac{15}{2}}{\left(\frac{1}{2}\right)^{-3}}$$

Multiplica \frac{9}{4} e \frac{4}{7} para obter \frac{9}{7}.

$$\frac{9}{7}\times \frac{\frac{4}{5}\times \frac{15}{2}}{\left(\frac{1}{2}\right)^{-3}}$$

Multiplica \frac{4}{5} e \frac{15}{2} para obter 6.

$$\frac{9}{7}\times \frac{6}{\left(\frac{1}{2}\right)^{-3}}$$

Calcula \frac{1}{2} á potencia de -3 e obtén 8.

$$\frac{9}{7}\times \frac{6}{8}$$

Reduce a fracción \frac{6}{8} a termos máis baixos extraendo e cancelando 2.

$$\frac{9}{7}\times \frac{3}{4}$$

Multiplica \frac{9}{7} e \frac{3}{4} para obter \frac{27}{28}.

$$\frac{27}{28}$$

Factorizar

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 7} = 0.9642857142857143$$