Solve [(2-13/5)^2+(5/8-3/4)-(6/5*frac{1}{3})^4*(7frac{1}{2})^3]:(5-frac{6}{5})=

$$[ ( 2 - 1 \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 5 } { 8 } - \frac { 3 } { 4 } ) - ( \frac { 6 } { 5 } \cdot \frac { 1 } { 3 } ) ^ { 4 } \cdot ( 7 \frac { 1 } { 2 } ) ^ { 3 } ] : ( 5 - \frac { 6 } { 5 } ) =$$

Evaluate

$$-\frac{2153}{760}\approx -2.832894737$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\left(2-\frac{5+3}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Add 5 and 3 to get 8.

$$\frac{\left(2-\frac{8}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Subtract \frac{8}{5} from 2 to get \frac{2}{5}.

$$\frac{\left(\frac{2}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{\frac{4}{25}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Add \frac{4}{25} and \frac{5}{8} to get \frac{157}{200}.

$$\frac{\frac{157}{200}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Subtract \frac{3}{4} from \frac{157}{200} to get \frac{7}{200}.

$$\frac{\frac{7}{200}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Multiply \frac{6}{5} and \frac{1}{3} to get \frac{2}{5}.

$$\frac{\frac{7}{200}-\left(\frac{2}{5}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculate \frac{2}{5} to the power of 4 and get \frac{16}{625}.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{14+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{15}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculate \frac{15}{2} to the power of 3 and get \frac{3375}{8}.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \frac{3375}{8}}{5-\frac{6}{5}}$$

Multiply \frac{16}{625} and \frac{3375}{8} to get \frac{54}{5}.

$$\frac{\frac{7}{200}-\frac{54}{5}}{5-\frac{6}{5}}$$

Subtract \frac{54}{5} from \frac{7}{200} to get -\frac{2153}{200}.

$$\frac{-\frac{2153}{200}}{5-\frac{6}{5}}$$

Subtract \frac{6}{5} from 5 to get \frac{19}{5}.

$$\frac{-\frac{2153}{200}}{\frac{19}{5}}$$

Divide -\frac{2153}{200} by \frac{19}{5} by multiplying -\frac{2153}{200} by the reciprocal of \frac{19}{5}.

$$-\frac{2153}{200}\times \frac{5}{19}$$

Multiply -\frac{2153}{200} and \frac{5}{19} to get -\frac{2153}{760}.

$$-\frac{2153}{760}$$

Factor

$$-\frac{2153}{760} = -2\frac{633}{760} = -2.832894736842105$$