Solve (-1/2)^3+(-2/5)^2div(-8/125)

$$( - \frac { 1 } { 2 } ) ^ { 3 } + ( - \frac { 2 } { 5 } ) ^ { 2 } \div ( - \frac { 8 } { 125 } )$$

Evaluate

$$-\frac{21}{8}=-2.625$$

Solution Steps

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

$$-\frac{1}{8}+\frac{\left(-\frac{2}{5}\right)^{2}}{-\frac{8}{125}}$$

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

$$-\frac{1}{8}+\frac{\frac{4}{25}}{-\frac{8}{125}}$$

Divide \frac{4}{25} by -\frac{8}{125} by multiplying \frac{4}{25} by the reciprocal of -\frac{8}{125}.

$$-\frac{1}{8}+\frac{4}{25}\left(-\frac{125}{8}\right)$$

Multiply \frac{4}{25} times -\frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{8}+\frac{4\left(-125\right)}{25\times 8}$$

Do the multiplications in the fraction \frac{4\left(-125\right)}{25\times 8}.

$$-\frac{1}{8}+\frac{-500}{200}$$

Reduce the fraction \frac{-500}{200} to lowest terms by extracting and canceling out 100.

$$-\frac{1}{8}-\frac{5}{2}$$

Least common multiple of 8 and 2 is 8. Convert -\frac{1}{8} and \frac{5}{2} to fractions with denominator 8.

$$-\frac{1}{8}-\frac{20}{8}$$

Since -\frac{1}{8} and \frac{20}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-20}{8}$$

Subtract 20 from -1 to get -21.

$$-\frac{21}{8}$$

Factor

$$-\frac{21}{8} = -2\frac{5}{8} = -2.625$$