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

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

Avaliar

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

Passos Para a Resolução

Calcule 8 elevado a -1 e obtenha \frac{1}{8}.

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

Calcule \frac{2}{3} elevado a -2 e obtenha \frac{9}{4}.

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

Some \frac{1}{8} e \frac{9}{4} para obter \frac{19}{8}.

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

Calcule 5 elevado a 0 e obtenha 1.

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

Subtraia 1 de \frac{19}{8} para obter \frac{11}{8}.

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

Calcule \frac{2}{3} elevado a -2 e obtenha \frac{9}{4}.

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

Calcule 4 elevado a -1 e obtenha \frac{1}{4}.

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

Some \frac{9}{4} e \frac{1}{4} para obter \frac{5}{2}.

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

Calcule 7 elevado a 0 e obtenha 1.

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

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

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

Divida \frac{11}{8} por \frac{3}{2} ao multiplicar \frac{11}{8} pelo recíproco de \frac{3}{2}.

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

Multiplique \frac{11}{8} e \frac{2}{3} para obter \frac{11}{12}.

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

Some \frac{11}{12} e \frac{31}{21} para obter \frac{67}{28}.

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

Fatorizar

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