Solve left(1/5-3/4left(16/7-frac{2/9}{frac{5}{6}+frac{11}{9}*frac{2}{33}divfrac{1}{6}-frac{11}{9}}{left(frac{3}{7}*frac{14}{9}divfrac{2}{3}-frac{1}{4}right)}^2right)left(frac{1}{3}+{left(frac{5}{3}right)}^2right)right){left(frac{6}{7}right)}^2

$$\left( \frac{ 1 }{ 5 } - \frac{ 3 }{ 4 } \left( \frac{ 16 }{ 7 } - \frac{ \frac{ 2 }{ 9 } }{ \frac{ 5 }{ 6 } + \frac{ 11 }{ 9 } \times \frac{ 2 }{ 33 } \div \frac{ 1 }{ 6 } - \frac{ 11 }{ 9 } } { \left( \frac{ 3 }{ 7 } \times \frac{ 14 }{ 9 } \div \frac{ 2 }{ 3 } - \frac{ 1 }{ 4 } \right) }^{ 2 } \right) \left( \frac{ 1 }{ 3 } + { \left( \frac{ 5 }{ 3 } \right) }^{ 2 } \right) \right) { \left( \frac{ 6 }{ 7 } \right) }^{ 2 }$$

Evaluate

$$\frac{3}{35}\approx 0.085714286$$

Solution Steps

Multiply \frac{11}{9} and \frac{2}{33} to get \frac{2}{27}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{5}{6}+\frac{\frac{2}{27}}{\frac{1}{6}}-\frac{11}{9}}\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Divide \frac{2}{27} by \frac{1}{6} by multiplying \frac{2}{27} by the reciprocal of \frac{1}{6}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{5}{6}+\frac{2}{27}\times 6-\frac{11}{9}}\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{2}{27} and 6 to get \frac{4}{9}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{5}{6}+\frac{4}{9}-\frac{11}{9}}\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Add \frac{5}{6} and \frac{4}{9} to get \frac{23}{18}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{23}{18}-\frac{11}{9}}\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{11}{9} from \frac{23}{18} to get \frac{1}{18}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{1}{18}}\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Divide \frac{2}{9} by \frac{1}{18} by multiplying \frac{2}{9} by the reciprocal of \frac{1}{18}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{2}{9}\times 18\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{2}{9} and 18 to get 4.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-4\left(\frac{\frac{3}{7}\times \frac{14}{9}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{3}{7} and \frac{14}{9} to get \frac{2}{3}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-4\left(\frac{\frac{2}{3}}{\frac{2}{3}}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Divide \frac{2}{3} by \frac{2}{3} to get 1.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-4\left(1-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

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

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-4\times \left(\frac{3}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-4\times \frac{9}{16}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply 4 and \frac{9}{16} to get \frac{9}{4}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{9}{4}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{9}{4} from \frac{16}{7} to get \frac{1}{28}.

$$\left(\frac{1}{5}-\frac{3}{4}\times \frac{1}{28}\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{3}{4} and \frac{1}{28} to get \frac{3}{112}.

$$\left(\frac{1}{5}-\frac{3}{112}\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\left(\frac{1}{5}-\frac{3}{112}\left(\frac{1}{3}+\frac{25}{9}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Add \frac{1}{3} and \frac{25}{9} to get \frac{28}{9}.

$$\left(\frac{1}{5}-\frac{3}{112}\times \frac{28}{9}\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{3}{112} and \frac{28}{9} to get \frac{1}{12}.

$$\left(\frac{1}{5}-\frac{1}{12}\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{1}{12} from \frac{1}{5} to get \frac{7}{60}.

$$\frac{7}{60}\times \left(\frac{6}{7}\right)^{2}$$

Calculate \frac{6}{7} to the power of 2 and get \frac{36}{49}.

$$\frac{7}{60}\times \frac{36}{49}$$

Multiply \frac{7}{60} and \frac{36}{49} to get \frac{3}{35}.

$$\frac{3}{35}$$

Factor

$$\frac{3}{5 \cdot 7} = 0.08571428571428572$$