Solve 2^-1-2/3(1-1/2)^2+sqrt[3]{-frac{1/8}}{2/3-(1-frac{3}{4})}

$$\frac { 2 ^ { - 1 } - \frac { 2 } { 3 } ( 1 - \frac { 1 } { 2 } ) ^ { 2 } + \sqrt[ 3 ] { - \frac { 1 } { 8 } } } { \frac { 2 } { 3 } - ( 1 - \frac { 3 } { 4 } ) }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

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

$$\frac{\frac{1}{2}-\frac{2}{3}\left(1-\frac{1}{2}\right)^{2}+\sqrt[3]{-\frac{1}{8}}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

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

$$\frac{\frac{1}{2}-\frac{2}{3}\times \left(\frac{1}{2}\right)^{2}+\sqrt[3]{-\frac{1}{8}}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

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

$$\frac{\frac{1}{2}-\frac{2}{3}\times \frac{1}{4}+\sqrt[3]{-\frac{1}{8}}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

Multiply \frac{2}{3} and \frac{1}{4} to get \frac{1}{6}.

$$\frac{\frac{1}{2}-\frac{1}{6}+\sqrt[3]{-\frac{1}{8}}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

Subtract \frac{1}{6} from \frac{1}{2} to get \frac{1}{3}.

$$\frac{\frac{1}{3}+\sqrt[3]{-\frac{1}{8}}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

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

Subtract \frac{1}{2} from \frac{1}{3} to get -\frac{1}{6}.

$$\frac{-\frac{1}{6}}{\frac{2}{3}-\left(1-\frac{3}{4}\right)}$$

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

$$\frac{-\frac{1}{6}}{\frac{2}{3}-\frac{1}{4}}$$

Subtract \frac{1}{4} from \frac{2}{3} to get \frac{5}{12}.

$$\frac{-\frac{1}{6}}{\frac{5}{12}}$$

Divide -\frac{1}{6} by \frac{5}{12} by multiplying -\frac{1}{6} by the reciprocal of \frac{5}{12}.

$$-\frac{1}{6}\times \frac{12}{5}$$

Multiply -\frac{1}{6} and \frac{12}{5} to get -\frac{2}{5}.

$$-\frac{2}{5}$$

Factor

$$-\frac{2}{5} = -0.4$$