Solve {1/5-3/4*[16/7-2/9:(frac{5}{6}+frac{11}{9}*frac{2}{33}*frac{1}{6}-frac{11}{9})*(frac{3}{7}*frac{14}{9}*frac{2}{3}-frac{1}{4})^2]*[frac{1}{3}+(frac{5}{3})^2]}*(frac{6}{7})^2

$$\{ \frac { 1 } { 5 } - \frac { 3 } { 4 } \cdot [ \frac { 16 } { 7 } - \frac { 2 } { 9 } : ( \frac { 5 } { 6 } + \frac { 11 } { 9 } \cdot \frac { 2 } { 33 } \cdot \frac { 1 } { 6 } - \frac { 11 } { 9 } ) \cdot ( \frac { 3 } { 7 } \cdot \frac { 14 } { 9 } \cdot \frac { 2 } { 3 } - \frac { 1 } { 4 } ) ^ { 2 } ] \cdot [ \frac { 1 } { 3 } + ( \frac { 5 } { 3 } ) ^ { 2 } ] \} \cdot ( \frac { 6 } { 7 } ) ^ { 2 }$$

Evaluate

$$-\frac{24401}{6405}\approx -3.809679938$$

Solution Steps

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

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

Multiply \frac{2}{27} and \frac{1}{6} to get \frac{1}{81}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{5}{6}+\frac{1}{81}-\frac{11}{9}}\left(\frac{3}{7}\times \frac{14}{9}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Add \frac{5}{6} and \frac{1}{81} to get \frac{137}{162}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{\frac{137}{162}-\frac{11}{9}}\left(\frac{3}{7}\times \frac{14}{9}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{11}{9} from \frac{137}{162} to get -\frac{61}{162}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{\frac{2}{9}}{-\frac{61}{162}}\left(\frac{3}{7}\times \frac{14}{9}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Divide \frac{2}{9} by -\frac{61}{162} by multiplying \frac{2}{9} by the reciprocal of -\frac{61}{162}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\frac{2}{9}\left(-\frac{162}{61}\right)\left(\frac{3}{7}\times \frac{14}{9}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{2}{9} and -\frac{162}{61} to get -\frac{36}{61}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{36}{61}\left(\frac{3}{7}\times \frac{14}{9}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

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

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{36}{61}\left(\frac{2}{3}\times \frac{2}{3}-\frac{1}{4}\right)^{2}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{2}{3} and \frac{2}{3} to get \frac{4}{9}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{36}{61}\left(\frac{4}{9}-\frac{1}{4}\right)^{2}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{1}{4} from \frac{4}{9} to get \frac{7}{36}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{36}{61}\times \left(\frac{7}{36}\right)^{2}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Calculate \frac{7}{36} to the power of 2 and get \frac{49}{1296}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{36}{61}\times \frac{49}{1296}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply -\frac{36}{61} and \frac{49}{1296} to get -\frac{49}{2196}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}-\left(-\frac{49}{2196}\right)\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

The opposite of -\frac{49}{2196} is \frac{49}{2196}.

$$\left(\frac{1}{5}-\frac{3}{4}\left(\frac{16}{7}+\frac{49}{2196}\right)\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Add \frac{16}{7} and \frac{49}{2196} to get \frac{35479}{15372}.

$$\left(\frac{1}{5}-\frac{3}{4}\times \frac{35479}{15372}\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{3}{4} and \frac{35479}{15372} to get \frac{35479}{20496}.

$$\left(\frac{1}{5}-\frac{35479}{20496}\left(\frac{1}{3}+\left(\frac{5}{3}\right)^{2}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

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

$$\left(\frac{1}{5}-\frac{35479}{20496}\left(\frac{1}{3}+\frac{25}{9}\right)\right)\times \left(\frac{6}{7}\right)^{2}$$

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

$$\left(\frac{1}{5}-\frac{35479}{20496}\times \frac{28}{9}\right)\times \left(\frac{6}{7}\right)^{2}$$

Multiply \frac{35479}{20496} and \frac{28}{9} to get \frac{35479}{6588}.

$$\left(\frac{1}{5}-\frac{35479}{6588}\right)\times \left(\frac{6}{7}\right)^{2}$$

Subtract \frac{35479}{6588} from \frac{1}{5} to get -\frac{170807}{32940}.

$$-\frac{170807}{32940}\times \left(\frac{6}{7}\right)^{2}$$

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

$$-\frac{170807}{32940}\times \frac{36}{49}$$

Multiply -\frac{170807}{32940} and \frac{36}{49} to get -\frac{24401}{6405}.

$$-\frac{24401}{6405}$$

Factor

$$-\frac{24401}{6405} = -3\frac{5186}{6405} = -3.80967993754879$$