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

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

Evaluate

$$\frac{67}{28}\approx 2.392857143$$

Solution Steps

Calculate 8 to the power of -1 and get \frac{1}{8}.

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

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

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

Add \frac{1}{8} and \frac{9}{4} to get \frac{19}{8}.

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

Calculate 5 to the power of 0 and get 1.

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

Subtract 1 from \frac{19}{8} to get \frac{11}{8}.

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

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

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

Calculate 4 to the power of -1 and get \frac{1}{4}.

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

Add \frac{9}{4} and \frac{1}{4} to get \frac{5}{2}.

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

Calculate 7 to the power of 0 and get 1.

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

Subtract 1 from \frac{5}{2} to get \frac{3}{2}.

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

Divide \frac{11}{8} by \frac{3}{2} by multiplying \frac{11}{8} by the reciprocal of \frac{3}{2}.

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

Multiply \frac{11}{8} and \frac{2}{3} to get \frac{11}{12}.

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

Add \frac{11}{12} and \frac{31}{21} to get \frac{67}{28}.

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

Factor

$$\frac{67}{2 ^ {2} \cdot 7} = 2\frac{11}{28} = 2.392857142857143$$