Solve (-1/2/-2)(2*(-1/2))^2-(-frac{1/2}{-2})^3

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

Evaluate

$$\frac{15}{64}=0.234375$$

Solution Steps

Express \frac{-\frac{1}{2}}{-2} as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-1}{-4} can be simplified to \frac{1}{4} by removing the negative sign from both the numerator and the denominator.

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

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

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

Calculate -1 to the power of 2 and get 1.

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

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

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

Express \frac{-\frac{1}{2}}{-2} as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-1}{-4} can be simplified to \frac{1}{4} by removing the negative sign from both the numerator and the denominator.

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

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{1}{4}-\frac{1}{64}$$

Subtract \frac{1}{64} from \frac{1}{4} to get \frac{15}{64}.

$$\frac{15}{64}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {6}} = 0.234375$$