Solve {(1+3/4-1/2)^2:[1-(5/4-1/2)]^2*(frac{2}{5}:frac{5}{4})*frac{1}{14}}^2

$$\{ ( 1 + \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } : [ 1 - ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ] ^ { 2 } \cdot ( \frac { 2 } { 5 } : \frac { 5 } { 4 } ) \cdot \frac { 1 } { 14 } \} ^ { 2 }$$

Evaluate

$$\frac{16}{49}\approx 0.326530612$$

Solution Steps

Add 1 and \frac{3}{4} to get \frac{7}{4}.

$$\left(\frac{\left(\frac{7}{4}-\frac{1}{2}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Subtract \frac{1}{2} from \frac{7}{4} to get \frac{5}{4}.

$$\left(\frac{\left(\frac{5}{4}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\left(\frac{\frac{25}{16}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Subtract \frac{1}{2} from \frac{5}{4} to get \frac{3}{4}.

$$\left(\frac{\frac{25}{16}}{\left(1-\frac{3}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Subtract \frac{3}{4} from 1 to get \frac{1}{4}.

$$\left(\frac{\frac{25}{16}}{\left(\frac{1}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\left(\frac{\frac{25}{16}}{\frac{1}{16}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Divide \frac{25}{16} by \frac{1}{16} by multiplying \frac{25}{16} by the reciprocal of \frac{1}{16}.

$$\left(\frac{25}{16}\times 16\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Multiply \frac{25}{16} and 16 to get 25.

$$\left(25\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Divide \frac{2}{5} by \frac{5}{4} by multiplying \frac{2}{5} by the reciprocal of \frac{5}{4}.

$$\left(25\times \frac{2}{5}\times \frac{4}{5}\times \frac{1}{14}\right)^{2}$$

Multiply \frac{2}{5} and \frac{4}{5} to get \frac{8}{25}.

$$\left(25\times \frac{8}{25}\times \frac{1}{14}\right)^{2}$$

Multiply 25 and \frac{8}{25} to get 8.

$$\left(8\times \frac{1}{14}\right)^{2}$$

Multiply 8 and \frac{1}{14} to get \frac{4}{7}.

$$\left(\frac{4}{7}\right)^{2}$$

Calculate \frac{4}{7} to the power of 2 and get \frac{16}{49}.

$$\frac{16}{49}$$

Factor

$$\frac{2 ^ {4}}{7 ^ {2}} = 0.32653061224489793$$