Solve {[(3/5+1/2-5/4)^2:(-3/20)^2+frac{5}{8}-frac{9}{2}]-frac{1}{8}}:(-frac{1}{3})^2=

$$\{ [ ( \frac { 3 } { 5 } + \frac { 1 } { 2 } - \frac { 5 } { 4 } ) ^ { 2 } : ( - \frac { 3 } { 20 } ) ^ { 2 } + \frac { 5 } { 8 } - \frac { 9 } { 2 } ] - \frac { 1 } { 8 } \} : ( - \frac { 1 } { 3 } ) ^ { 2 } =$$

Evaluate

$$-27$$

Solution Steps

Add \frac{3}{5} and \frac{1}{2} to get \frac{11}{10}.

$$\frac{\frac{\left(\frac{11}{10}-\frac{5}{4}\right)^{2}}{\left(-\frac{3}{20}\right)^{2}}+\frac{5}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Subtract \frac{5}{4} from \frac{11}{10} to get -\frac{3}{20}.

$$\frac{\frac{\left(-\frac{3}{20}\right)^{2}}{\left(-\frac{3}{20}\right)^{2}}+\frac{5}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Calculate -\frac{3}{20} to the power of 2 and get \frac{9}{400}.

$$\frac{\frac{\frac{9}{400}}{\left(-\frac{3}{20}\right)^{2}}+\frac{5}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Calculate -\frac{3}{20} to the power of 2 and get \frac{9}{400}.

$$\frac{\frac{\frac{9}{400}}{\frac{9}{400}}+\frac{5}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Divide \frac{9}{400} by \frac{9}{400} to get 1.

$$\frac{1+\frac{5}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Add 1 and \frac{5}{8} to get \frac{13}{8}.

$$\frac{\frac{13}{8}-\frac{9}{2}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Subtract \frac{9}{2} from \frac{13}{8} to get -\frac{23}{8}.

$$\frac{-\frac{23}{8}-\frac{1}{8}}{\left(-\frac{1}{3}\right)^{2}}$$

Subtract \frac{1}{8} from -\frac{23}{8} to get -3.

$$\frac{-3}{\left(-\frac{1}{3}\right)^{2}}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{-3}{\frac{1}{9}}$$

Divide -3 by \frac{1}{9} by multiplying -3 by the reciprocal of \frac{1}{9}.

$$-3\times 9$$

Multiply -3 and 9 to get -27.

$$-27$$

Factor

$$-27$$