Resolver (27/125)^frac{1{3}}*[(3/2)^-2div(2/5)^3]-4(3/7)^0

$$( \frac { 27 } { 125 } ) ^ { \frac { 1 } { 3 } } \times [ ( \frac { 3 } { 2 } ) ^ { - 2 } \div ( \frac { 2 } { 5 } ) ^ { 3 } ] - 4 ( \frac { 3 } { 7 } ) ^ { 0 }$$

Calcular

$$\frac{1}{6}\approx 0.166666667$$

Pasos da solución

Calcula \frac{27}{125} á potencia de \frac{1}{3} e obtén \frac{3}{5}.

$$\frac{3}{5}\times \frac{\left(\frac{3}{2}\right)^{-2}}{\left(\frac{2}{5}\right)^{3}}-4\times \left(\frac{3}{7}\right)^{0}$$

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

$$\frac{3}{5}\times \frac{\frac{4}{9}}{\left(\frac{2}{5}\right)^{3}}-4\times \left(\frac{3}{7}\right)^{0}$$

Calcula \frac{2}{5} á potencia de 3 e obtén \frac{8}{125}.

$$\frac{3}{5}\times \frac{\frac{4}{9}}{\frac{8}{125}}-4\times \left(\frac{3}{7}\right)^{0}$$

Divide \frac{4}{9} entre \frac{8}{125} mediante a multiplicación de \frac{4}{9} polo recíproco de \frac{8}{125}.

$$\frac{3}{5}\times \frac{4}{9}\times \frac{125}{8}-4\times \left(\frac{3}{7}\right)^{0}$$

Multiplica \frac{4}{9} e \frac{125}{8} para obter \frac{125}{18}.

$$\frac{3}{5}\times \frac{125}{18}-4\times \left(\frac{3}{7}\right)^{0}$$

Multiplica \frac{3}{5} e \frac{125}{18} para obter \frac{25}{6}.

$$\frac{25}{6}-4\times \left(\frac{3}{7}\right)^{0}$$

Calcula \frac{3}{7} á potencia de 0 e obtén 1.

$$\frac{25}{6}-4\times 1$$

Multiplica 4 e 1 para obter 4.

$$\frac{25}{6}-4$$

Resta 4 de \frac{25}{6} para obter \frac{1}{6}.

$$\frac{1}{6}$$

Factorizar

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$