Solve (2-1/5)^2/(3-frac{4{4})^-1}+(6/7*frac{5/4-frac{1}{7}+frac{1}{2})^3}{(frac{1}{2}-frac{1}{3}*frac{1}{4}div5)}-4frac{4}{6}

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

Evaluate

$$\frac{5852792}{746025}\approx 7.845302771$$

Solution Steps

Divide 4 by 4 to get 1.

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

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

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

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

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

Subtract 1 from 3 to get 2.

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

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

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

Divide \frac{81}{25} by \frac{1}{2} by multiplying \frac{81}{25} by the reciprocal of \frac{1}{2}.

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

Multiply \frac{81}{25} and 2 to get \frac{162}{25}.

$$\frac{162}{25}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

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

$$\frac{162}{25}+\frac{\left(\frac{15}{14}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Subtract \frac{1}{7} from \frac{15}{14} to get \frac{13}{14}.

$$\frac{162}{25}+\frac{\left(\frac{13}{14}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Add \frac{13}{14} and \frac{1}{2} to get \frac{10}{7}.

$$\frac{162}{25}+\frac{\left(\frac{10}{7}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Calculate \frac{10}{7} to the power of 3 and get \frac{1000}{343}.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

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

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{\frac{1}{12}}{5}}-\frac{4\times 6+4}{6}$$

Express \frac{\frac{1}{12}}{5} as a single fraction.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{1}{12\times 5}}-\frac{4\times 6+4}{6}$$

Multiply 12 and 5 to get 60.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{1}{60}}-\frac{4\times 6+4}{6}$$

Subtract \frac{1}{60} from \frac{1}{2} to get \frac{29}{60}.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{29}{60}}-\frac{4\times 6+4}{6}$$

Divide \frac{1000}{343} by \frac{29}{60} by multiplying \frac{1000}{343} by the reciprocal of \frac{29}{60}.

$$\frac{162}{25}+\frac{1000}{343}\times \frac{60}{29}-\frac{4\times 6+4}{6}$$

Multiply \frac{1000}{343} and \frac{60}{29} to get \frac{60000}{9947}.

$$\frac{162}{25}+\frac{60000}{9947}-\frac{4\times 6+4}{6}$$

Add \frac{162}{25} and \frac{60000}{9947} to get \frac{3111414}{248675}.

$$\frac{3111414}{248675}-\frac{4\times 6+4}{6}$$

Multiply 4 and 6 to get 24.

$$\frac{3111414}{248675}-\frac{24+4}{6}$$

Add 24 and 4 to get 28.

$$\frac{3111414}{248675}-\frac{28}{6}$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3111414}{248675}-\frac{14}{3}$$

Subtract \frac{14}{3} from \frac{3111414}{248675} to get \frac{5852792}{746025}.

$$\frac{5852792}{746025}$$

Factor

$$\frac{2 ^ {3} \cdot 11 \cdot 66509}{3 \cdot 5 ^ {2} \cdot 7 ^ {3} \cdot 29} = 7\frac{630617}{746025} = 7.845302771354848$$