Solve (1-1/2)^4:{[(3/7+1/6-5/14)*(5+frac{1}{4})-frac{1}{2}]:(frac{3}{4})^2-frac{1}{4}}^3-frac{1}{2}

$$( 1 - \frac { 1 } { 2 } ) ^ { 4 } : \{ [ ( \frac { 3 } { 7 } + \frac { 1 } { 6 } - \frac { 5 } { 14 } ) \cdot ( 5 + \frac { 1 } { 4 } ) - \frac { 1 } { 2 } ] : ( \frac { 3 } { 4 } ) ^ { 2 } - \frac { 1 } { 4 } \} ^ { 3 } - \frac { 1 } { 2 }$$

Evaluate

$$-\frac{1981}{4394}\approx -0.450842057$$

Solution Steps

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

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

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

$$\frac{\frac{1}{16}}{\left(\frac{\left(\frac{3}{7}+\frac{1}{6}-\frac{5}{14}\right)\left(5+\frac{1}{4}\right)-\frac{1}{2}}{\left(\frac{3}{4}\right)^{2}}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Add \frac{3}{7} and \frac{1}{6} to get \frac{25}{42}.

$$\frac{\frac{1}{16}}{\left(\frac{\left(\frac{25}{42}-\frac{5}{14}\right)\left(5+\frac{1}{4}\right)-\frac{1}{2}}{\left(\frac{3}{4}\right)^{2}}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Subtract \frac{5}{14} from \frac{25}{42} to get \frac{5}{21}.

$$\frac{\frac{1}{16}}{\left(\frac{\frac{5}{21}\left(5+\frac{1}{4}\right)-\frac{1}{2}}{\left(\frac{3}{4}\right)^{2}}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Add 5 and \frac{1}{4} to get \frac{21}{4}.

$$\frac{\frac{1}{16}}{\left(\frac{\frac{5}{21}\times \frac{21}{4}-\frac{1}{2}}{\left(\frac{3}{4}\right)^{2}}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Multiply \frac{5}{21} and \frac{21}{4} to get \frac{5}{4}.

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

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

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

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\frac{1}{16}}{\left(\frac{\frac{3}{4}}{\frac{9}{16}}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Divide \frac{3}{4} by \frac{9}{16} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{16}.

$$\frac{\frac{1}{16}}{\left(\frac{3}{4}\times \frac{16}{9}-\frac{1}{4}\right)^{3}}-\frac{1}{2}$$

Multiply \frac{3}{4} and \frac{16}{9} to get \frac{4}{3}.

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

Subtract \frac{1}{4} from \frac{4}{3} to get \frac{13}{12}.

$$\frac{\frac{1}{16}}{\left(\frac{13}{12}\right)^{3}}-\frac{1}{2}$$

Calculate \frac{13}{12} to the power of 3 and get \frac{2197}{1728}.

$$\frac{\frac{1}{16}}{\frac{2197}{1728}}-\frac{1}{2}$$

Divide \frac{1}{16} by \frac{2197}{1728} by multiplying \frac{1}{16} by the reciprocal of \frac{2197}{1728}.

$$\frac{1}{16}\times \frac{1728}{2197}-\frac{1}{2}$$

Multiply \frac{1}{16} and \frac{1728}{2197} to get \frac{108}{2197}.

$$\frac{108}{2197}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{108}{2197} to get -\frac{1981}{4394}.

$$-\frac{1981}{4394}$$

Factor

$$-\frac{1981}{4394} = -0.4508420573509331$$