Solve (1/2)^3-(1/2-3/4)^2-4

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

Evaluate

$$-\frac{63}{16}=-3.9375$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

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

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

$$\frac{1}{8}-\left(-\frac{1}{4}\right)^{2}-4$$

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

$$\frac{1}{8}-\frac{1}{16}-4$$

Subtract \frac{1}{16} from \frac{1}{8} to get \frac{1}{16}.

$$\frac{1}{16}-4$$

Subtract 4 from \frac{1}{16} to get -\frac{63}{16}.

$$-\frac{63}{16}$$

Factor

$$-\frac{63}{16} = -3\frac{15}{16} = -3.9375$$