Resolver (8/27)^-frac{3{3}}*(25/4)^frac{1{2}}*(4/9)^0+(125/64)^frac{1{3}}

$$( \frac { 8 } { 27 } ) ^ { - \frac { 3 } { 3 } } \times ( \frac { 25 } { 4 } ) ^ { \frac { 1 } { 2 } } \times ( \frac { 4 } { 9 } ) ^ { 0 } + ( \frac { 125 } { 64 } ) ^ { \frac { 1 } { 3 } }$$

Calcular

$$\frac{155}{16}=9.6875$$

Pasos da solución

Divide 3 entre 3 para obter 1.

$$\left(\frac{8}{27}\right)^{-1}\times \left(\frac{25}{4}\right)^{\frac{1}{2}}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calcula \frac{8}{27} á potencia de -1 e obtén \frac{27}{8}.

$$\frac{27}{8}\times \left(\frac{25}{4}\right)^{\frac{1}{2}}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calcula \frac{25}{4} á potencia de \frac{1}{2} e obtén \frac{5}{2}.

$$\frac{27}{8}\times \frac{5}{2}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Multiplica \frac{27}{8} e \frac{5}{2} para obter \frac{135}{16}.

$$\frac{135}{16}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calcula \frac{4}{9} á potencia de 0 e obtén 1.

$$\frac{135}{16}\times 1+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Multiplica \frac{135}{16} e 1 para obter \frac{135}{16}.

$$\frac{135}{16}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calcula \frac{125}{64} á potencia de \frac{1}{3} e obtén \frac{5}{4}.

$$\frac{135}{16}+\frac{5}{4}$$

Suma \frac{135}{16} e \frac{5}{4} para obter \frac{155}{16}.

$$\frac{155}{16}$$

Factorizar

$$\frac{5 \cdot 31}{2 ^ {4}} = 9\frac{11}{16} = 9.6875$$