Solve -(-2/3)^3-15/4*(-2/3)

$$- ( - \frac { 2 } { 3 } ) ^ { 3 } - \frac { 15 } { 4 } \times ( - \frac { 2 } { 3 } )$$

Evaluate

$$\frac{151}{54}\approx 2.796296296$$

Solution Steps

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

$$-\left(-\frac{8}{27}\right)-\frac{15}{4}\left(-\frac{2}{3}\right)$$

The opposite of -\frac{8}{27} is \frac{8}{27}.

$$\frac{8}{27}-\frac{15}{4}\left(-\frac{2}{3}\right)$$

Multiply \frac{15}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{27}-\frac{15\left(-2\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{15\left(-2\right)}{4\times 3}.

$$\frac{8}{27}-\frac{-30}{12}$$

Reduce the fraction \frac{-30}{12} to lowest terms by extracting and canceling out 6.

$$\frac{8}{27}-\left(-\frac{5}{2}\right)$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$\frac{8}{27}+\frac{5}{2}$$

Least common multiple of 27 and 2 is 54. Convert \frac{8}{27} and \frac{5}{2} to fractions with denominator 54.

$$\frac{16}{54}+\frac{135}{54}$$

Since \frac{16}{54} and \frac{135}{54} have the same denominator, add them by adding their numerators.

$$\frac{16+135}{54}$$

Add 16 and 135 to get 151.

$$\frac{151}{54}$$

Factor

$$\frac{151}{2 \cdot 3 ^ {3}} = 2\frac{43}{54} = 2.7962962962962963$$