Solve =(2/5)^3+(-1/2)^3+(-1/6)^3-3(2/3)(-frac{1}{2})(-frac{1}{6})

$$= ( \frac { 2 } { 5 } ) ^ { 3 } + ( - \frac { 1 } { 2 } ) ^ { 3 } + ( - \frac { 1 } { 6 } ) ^ { 3 } - 3 ( \frac { 2 } { 3 } ) ( - \frac { 1 } { 2 } ) ( - \frac { 1 } { 6 } )$$

Evaluate

$$-\frac{784}{3375}\approx -0.232296296$$

Solution Steps

Calculate \frac{2}{5} to the power of 3 and get \frac{8}{125}.

$$\frac{8}{125}+\left(-\frac{1}{2}\right)^{3}+\left(-\frac{1}{6}\right)^{3}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

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

$$\frac{8}{125}-\frac{1}{8}+\left(-\frac{1}{6}\right)^{3}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Least common multiple of 125 and 8 is 1000. Convert \frac{8}{125} and \frac{1}{8} to fractions with denominator 1000.

$$\frac{64}{1000}-\frac{125}{1000}+\left(-\frac{1}{6}\right)^{3}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Since \frac{64}{1000} and \frac{125}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-125}{1000}+\left(-\frac{1}{6}\right)^{3}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Subtract 125 from 64 to get -61.

$$-\frac{61}{1000}+\left(-\frac{1}{6}\right)^{3}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Calculate -\frac{1}{6} to the power of 3 and get -\frac{1}{216}.

$$-\frac{61}{1000}-\frac{1}{216}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Least common multiple of 1000 and 216 is 27000. Convert -\frac{61}{1000} and \frac{1}{216} to fractions with denominator 27000.

$$-\frac{1647}{27000}-\frac{125}{27000}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Since -\frac{1647}{27000} and \frac{125}{27000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1647-125}{27000}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Subtract 125 from -1647 to get -1772.

$$\frac{-1772}{27000}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Reduce the fraction \frac{-1772}{27000} to lowest terms by extracting and canceling out 4.

$$-\frac{443}{6750}-3\times \frac{2}{3}\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Cancel out 3 and 3.

$$-\frac{443}{6750}-2\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)$$

Cancel out 2 and 2.

$$-\frac{443}{6750}-\left(-\left(-\frac{1}{6}\right)\right)$$

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

$$-\frac{443}{6750}-\frac{1}{6}$$

Least common multiple of 6750 and 6 is 6750. Convert -\frac{443}{6750} and \frac{1}{6} to fractions with denominator 6750.

$$-\frac{443}{6750}-\frac{1125}{6750}$$

Since -\frac{443}{6750} and \frac{1125}{6750} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-443-1125}{6750}$$

Subtract 1125 from -443 to get -1568.

$$\frac{-1568}{6750}$$

Reduce the fraction \frac{-1568}{6750} to lowest terms by extracting and canceling out 2.

$$-\frac{784}{3375}$$

Factor

$$-\frac{784}{3375} = -0.2322962962962963$$