Solucionar 8^-1+{left(frac{2/3right)}^-2-5^0}{{left(2/3right)}^-2+4^-1-7^0}+31/21

$$\frac{ { 8 }^{ -1 } + { \left( \frac{ 2 }{ 3 } \right) }^{ -2 } - { 5 }^{ 0 } }{ { \left( \frac{ 2 }{ 3 } \right) }^{ -2 } + { 4 }^{ -1 } - { 7 }^{ 0 } } + \frac{ 31 }{ 21 }$$

Calcular

$$\frac{67}{28}\approx 2,392857143$$

Pasos de la solución

Calcula 8 a la potencia de -1 y obtiene \frac{1}{8}.

$$\frac{\frac{1}{8}+\left(\frac{2}{3}\right)^{-2}-5^{0}}{\left(\frac{2}{3}\right)^{-2}+4^{-1}-7^{0}}+\frac{31}{21}$$

Calcula \frac{2}{3} a la potencia de -2 y obtiene \frac{9}{4}.

$$\frac{\frac{1}{8}+\frac{9}{4}-5^{0}}{\left(\frac{2}{3}\right)^{-2}+4^{-1}-7^{0}}+\frac{31}{21}$$

Suma \frac{1}{8} y \frac{9}{4} para obtener \frac{19}{8}.

$$\frac{\frac{19}{8}-5^{0}}{\left(\frac{2}{3}\right)^{-2}+4^{-1}-7^{0}}+\frac{31}{21}$$

Calcula 5 a la potencia de 0 y obtiene 1.

$$\frac{\frac{19}{8}-1}{\left(\frac{2}{3}\right)^{-2}+4^{-1}-7^{0}}+\frac{31}{21}$$

Resta 1 de \frac{19}{8} para obtener \frac{11}{8}.

$$\frac{\frac{11}{8}}{\left(\frac{2}{3}\right)^{-2}+4^{-1}-7^{0}}+\frac{31}{21}$$

Calcula \frac{2}{3} a la potencia de -2 y obtiene \frac{9}{4}.

$$\frac{\frac{11}{8}}{\frac{9}{4}+4^{-1}-7^{0}}+\frac{31}{21}$$

Calcula 4 a la potencia de -1 y obtiene \frac{1}{4}.

$$\frac{\frac{11}{8}}{\frac{9}{4}+\frac{1}{4}-7^{0}}+\frac{31}{21}$$

Suma \frac{9}{4} y \frac{1}{4} para obtener \frac{5}{2}.

$$\frac{\frac{11}{8}}{\frac{5}{2}-7^{0}}+\frac{31}{21}$$

Calcula 7 a la potencia de 0 y obtiene 1.

$$\frac{\frac{11}{8}}{\frac{5}{2}-1}+\frac{31}{21}$$

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

$$\frac{\frac{11}{8}}{\frac{3}{2}}+\frac{31}{21}$$

Divide \frac{11}{8} por \frac{3}{2} al multiplicar \frac{11}{8} por el recíproco de \frac{3}{2}.

$$\frac{11}{8}\times \frac{2}{3}+\frac{31}{21}$$

Multiplica \frac{11}{8} y \frac{2}{3} para obtener \frac{11}{12}.

$$\frac{11}{12}+\frac{31}{21}$$

Suma \frac{11}{12} y \frac{31}{21} para obtener \frac{67}{28}.

$$\frac{67}{28}$$

Factorizar

$$\frac{67}{2 ^ {2} \cdot 7} = 2\frac{11}{28} = 2,392857142857143$$