Solve 2*(-2/3)^3+5*4/9-4*2/3

$$2 \times ( - \frac { 2 } { 3 } ) ^ { 3 } + 5 \times \frac { 4 } { 9 } - 4 \times \frac { 2 } { 3 }$$

Evaluate

$$-\frac{28}{27}\approx -1.037037037$$

Solution Steps

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$2\left(-\frac{8}{27}\right)+5\times \frac{4}{9}-4\times \frac{2}{3}$$

Express 2\left(-\frac{8}{27}\right) as a single fraction.

$$\frac{2\left(-8\right)}{27}+5\times \frac{4}{9}-4\times \frac{2}{3}$$

Multiply 2 and -8 to get -16.

$$\frac{-16}{27}+5\times \frac{4}{9}-4\times \frac{2}{3}$$

Fraction \frac{-16}{27} can be rewritten as -\frac{16}{27} by extracting the negative sign.

$$-\frac{16}{27}+5\times \frac{4}{9}-4\times \frac{2}{3}$$

Express 5\times \frac{4}{9} as a single fraction.

$$-\frac{16}{27}+\frac{5\times 4}{9}-4\times \frac{2}{3}$$

Multiply 5 and 4 to get 20.

$$-\frac{16}{27}+\frac{20}{9}-4\times \frac{2}{3}$$

Least common multiple of 27 and 9 is 27. Convert -\frac{16}{27} and \frac{20}{9} to fractions with denominator 27.

$$-\frac{16}{27}+\frac{60}{27}-4\times \frac{2}{3}$$

Since -\frac{16}{27} and \frac{60}{27} have the same denominator, add them by adding their numerators.

$$\frac{-16+60}{27}-4\times \frac{2}{3}$$

Add -16 and 60 to get 44.

$$\frac{44}{27}-4\times \frac{2}{3}$$

Express 4\times \frac{2}{3} as a single fraction.

$$\frac{44}{27}-\frac{4\times 2}{3}$$

Multiply 4 and 2 to get 8.

$$\frac{44}{27}-\frac{8}{3}$$

Least common multiple of 27 and 3 is 27. Convert \frac{44}{27} and \frac{8}{3} to fractions with denominator 27.

$$\frac{44}{27}-\frac{72}{27}$$

Since \frac{44}{27} and \frac{72}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-72}{27}$$

Subtract 72 from 44 to get -28.

$$-\frac{28}{27}$$

Factor

$$-\frac{28}{27} = -1\frac{1}{27} = -1.037037037037037$$