Solve (2-1/5)^2/(3-frac{2{9})^-7}:(6/7*frac{5/4-frac{2}{7}:frac{1}{2})^3}{(frac{1}{2}-frac{1}{3}*frac{1}{4}:frac{1}{5})}-5frac{1}{7}=

$$\frac { ( 2 - \frac { 1 } { 5 } ) ^ { 2 } } { ( 3 - \frac { 2 } { 9 } ) ^ { - 7 } } : \frac { ( \frac { 6 } { 7 } \cdot \frac { 5 } { 4 } - \frac { 2 } { 7 } : \frac { 1 } { 2 } ) ^ { 3 } } { ( \frac { 1 } { 2 } - \frac { 1 } { 3 } \cdot \frac { 1 } { 4 } : \frac { 1 } { 5 } ) } - 5 \frac { 1 } { 7 } =$$

Evaluate

$$\frac{3411591458}{1240029}\approx 2751.219090844$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate \frac{25}{9} to the power of -7 and get \frac{4782969}{6103515625}.

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\left(\frac{6}{7}\times \frac{5}{4}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

Multiply \frac{6}{7} and \frac{5}{4} to get \frac{15}{14}.

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\left(\frac{15}{14}-\frac{\frac{2}{7}}{\frac{1}{2}}\right)^{3}}-\frac{5\times 7+1}{7}$$

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

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\left(\frac{15}{14}-\frac{2}{7}\times 2\right)^{3}}-\frac{5\times 7+1}{7}$$

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

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\left(\frac{15}{14}-\frac{4}{7}\right)^{3}}-\frac{5\times 7+1}{7}$$

Subtract \frac{4}{7} from \frac{15}{14} to get \frac{1}{2}.

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\times \left(\frac{1}{2}\right)^{3}}-\frac{5\times 7+1}{7}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{\frac{27}{100}}{\frac{4782969}{6103515625}\times \frac{1}{8}}-\frac{5\times 7+1}{7}$$

Multiply \frac{4782969}{6103515625} and \frac{1}{8} to get \frac{4782969}{48828125000}.

$$\frac{\frac{27}{100}}{\frac{4782969}{48828125000}}-\frac{5\times 7+1}{7}$$

Divide \frac{27}{100} by \frac{4782969}{48828125000} by multiplying \frac{27}{100} by the reciprocal of \frac{4782969}{48828125000}.

$$\frac{27}{100}\times \frac{48828125000}{4782969}-\frac{5\times 7+1}{7}$$

Multiply \frac{27}{100} and \frac{48828125000}{4782969} to get \frac{488281250}{177147}.

$$\frac{488281250}{177147}-\frac{5\times 7+1}{7}$$

Multiply 5 and 7 to get 35.

$$\frac{488281250}{177147}-\frac{35+1}{7}$$

Add 35 and 1 to get 36.

$$\frac{488281250}{177147}-\frac{36}{7}$$

Subtract \frac{36}{7} from \frac{488281250}{177147} to get \frac{3411591458}{1240029}.

$$\frac{3411591458}{1240029}$$

Factor

$$\frac{2 \cdot 11 \cdot 79 \cdot 1962941}{3 ^ {11} \cdot 7} = 2751\frac{271679}{1240029} = 2751.2190908438433$$