Solve frac{{left(2-frac{1/5right)}^2}{{left(3-2/9right)}^-1}}{{left(6/7-frac{5/4-frac{frac{2}{7}}{frac{1}{2}}right)}^3}{frac{1}{2}-frac{1}{3}frac{1}{4}divfrac{1}{5}}}-5frac{1}{7}

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

Evaluate

$$-\frac{274612}{45927}\approx -5.979315$$

Solution Steps

Divide \frac{\left(2-\frac{1}{5}\right)^{2}}{\left(3-\frac{2}{9}\right)^{-1}} by \frac{\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{\frac{1}{5}}} by multiplying \frac{\left(2-\frac{1}{5}\right)^{2}}{\left(3-\frac{2}{9}\right)^{-1}} by the reciprocal of \frac{\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{\frac{1}{5}}}.

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

Subtract \frac{1}{5} from 2 to get \frac{9}{5}.

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

Calculate \frac{9}{5} to the power of 2 and get \frac{81}{25}.

$$\frac{\frac{81}{25}\left(\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{\frac{1}{5}}\right)}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Multiply \frac{1}{3} and \frac{1}{4} to get \frac{1}{12}.

$$\frac{\frac{81}{25}\left(\frac{1}{2}-\frac{\frac{1}{12}}{\frac{1}{5}}\right)}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Divide \frac{1}{12} by \frac{1}{5} by multiplying \frac{1}{12} by the reciprocal of \frac{1}{5}.

$$\frac{\frac{81}{25}\left(\frac{1}{2}-\frac{1}{12}\times 5\right)}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Multiply \frac{1}{12} and 5 to get \frac{5}{12}.

$$\frac{\frac{81}{25}\left(\frac{1}{2}-\frac{5}{12}\right)}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Subtract \frac{5}{12} from \frac{1}{2} to get \frac{1}{12}.

$$\frac{\frac{81}{25}\times \frac{1}{12}}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Multiply \frac{81}{25} and \frac{1}{12} to get \frac{27}{100}.

$$\frac{\frac{27}{100}}{\left(3-\frac{2}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Subtract \frac{2}{9} from 3 to get \frac{25}{9}.

$$\frac{\frac{27}{100}}{\left(\frac{25}{9}\right)^{-1}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Calculate \frac{25}{9} to the power of -1 and get \frac{9}{25}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(\frac{6}{7}-\frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Subtract \frac{5}{4} from \frac{6}{7} to get -\frac{11}{28}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(-\frac{11}{28}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Divide \frac{2}{7} by \frac{1}{2} by multiplying \frac{2}{7} by the reciprocal of \frac{1}{2}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(-\frac{11}{28}-\frac{2}{7}\times 2\right)^{3}}-\frac{5\times 7+1}{7}$$

Multiply \frac{2}{7} and 2 to get \frac{4}{7}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(-\frac{11}{28}-\frac{4}{7}\right)^{3}}-\frac{5\times 7+1}{7}$$

Subtract \frac{4}{7} from -\frac{11}{28} to get -\frac{27}{28}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(-\frac{27}{28}\right)^{3}}-\frac{5\times 7+1}{7}$$

Calculate -\frac{27}{28} to the power of 3 and get -\frac{19683}{21952}.

$$\frac{\frac{27}{100}}{\frac{9}{25}\left(-\frac{19683}{21952}\right)}-\frac{5\times 7+1}{7}$$

Multiply \frac{9}{25} and -\frac{19683}{21952} to get -\frac{177147}{548800}.

$$\frac{\frac{27}{100}}{-\frac{177147}{548800}}-\frac{5\times 7+1}{7}$$

Divide \frac{27}{100} by -\frac{177147}{548800} by multiplying \frac{27}{100} by the reciprocal of -\frac{177147}{548800}.

$$\frac{27}{100}\left(-\frac{548800}{177147}\right)-\frac{5\times 7+1}{7}$$

Multiply \frac{27}{100} and -\frac{548800}{177147} to get -\frac{5488}{6561}.

$$-\frac{5488}{6561}-\frac{5\times 7+1}{7}$$

Multiply 5 and 7 to get 35.

$$-\frac{5488}{6561}-\frac{35+1}{7}$$

Add 35 and 1 to get 36.

$$-\frac{5488}{6561}-\frac{36}{7}$$

Subtract \frac{36}{7} from -\frac{5488}{6561} to get -\frac{274612}{45927}.

$$-\frac{274612}{45927}$$

Factor

$$-\frac{274612}{45927} = -5\frac{44977}{45927} = -5.979314999891131$$