Solve left(1-5/6+4/3right){left(1-4/9/{left(2-left(1-frac{1{4}-frac{11}{6}right){left(-frac{13}{6}right)}^-1-1right)}^2}-{left(frac{9}{23}right)}^-1right)}^3+frac{1}{6}

$$\left( 1- \frac{ 5 }{ 6 } + \frac{ 4 }{ 3 } \right) { \left( \frac{ 1- \frac{ 4 }{ 9 } }{ { \left(2- \left( 1- \frac{ 1 }{ 4 } - \frac{ 11 }{ 6 } \right) { \left(- \frac{ 13 }{ 6 } \right) }^{ -1 } -1 \right) }^{ 2 } } - { \left( \frac{ 9 }{ 23 } \right) }^{ -1 } \right) }^{ 3 } + \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Subtract \frac{5}{6} from 1 to get \frac{1}{6}.

$$\left(\frac{1}{6}+\frac{4}{3}\right)\left(\frac{1-\frac{4}{9}}{\left(2-\left(1-\frac{1}{4}-\frac{11}{6}\right)\left(-\frac{13}{6}\right)^{-1}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Add \frac{1}{6} and \frac{4}{3} to get \frac{3}{2}.

$$\frac{3}{2}\left(\frac{1-\frac{4}{9}}{\left(2-\left(1-\frac{1}{4}-\frac{11}{6}\right)\left(-\frac{13}{6}\right)^{-1}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Subtract \frac{4}{9} from 1 to get \frac{5}{9}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(2-\left(1-\frac{1}{4}-\frac{11}{6}\right)\left(-\frac{13}{6}\right)^{-1}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(2-\left(\frac{3}{4}-\frac{11}{6}\right)\left(-\frac{13}{6}\right)^{-1}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Subtract \frac{11}{6} from \frac{3}{4} to get -\frac{13}{12}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(2-\left(-\frac{13}{12}\left(-\frac{13}{6}\right)^{-1}\right)-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Calculate -\frac{13}{6} to the power of -1 and get -\frac{6}{13}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(2-\left(-\frac{13}{12}\left(-\frac{6}{13}\right)\right)-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Multiply -\frac{13}{12} and -\frac{6}{13} to get \frac{1}{2}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(2-\frac{1}{2}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

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

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(\frac{3}{2}-1\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

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

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\left(\frac{1}{2}\right)^{2}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{2}\left(\frac{\frac{5}{9}}{\frac{1}{4}}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Divide \frac{5}{9} by \frac{1}{4} by multiplying \frac{5}{9} by the reciprocal of \frac{1}{4}.

$$\frac{3}{2}\left(\frac{5}{9}\times 4-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Multiply \frac{5}{9} and 4 to get \frac{20}{9}.

$$\frac{3}{2}\left(\frac{20}{9}-\left(\frac{9}{23}\right)^{-1}\right)^{3}+\frac{1}{6}$$

Calculate \frac{9}{23} to the power of -1 and get \frac{23}{9}.

$$\frac{3}{2}\left(\frac{20}{9}-\frac{23}{9}\right)^{3}+\frac{1}{6}$$

Subtract \frac{23}{9} from \frac{20}{9} to get -\frac{1}{3}.

$$\frac{3}{2}\left(-\frac{1}{3}\right)^{3}+\frac{1}{6}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\frac{3}{2}\left(-\frac{1}{27}\right)+\frac{1}{6}$$

Multiply \frac{3}{2} and -\frac{1}{27} to get -\frac{1}{18}.

$$-\frac{1}{18}+\frac{1}{6}$$

Add -\frac{1}{18} and \frac{1}{6} to get \frac{1}{9}.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$