Solve (-3/4)*[(-2)^3-(-2/3)-1/3]

$$( - \frac { 3 } { 4 } ) \times [ ( - 2 ) ^ { 3 } - ( - \frac { 2 } { 3 } ) - \frac { 1 } { 3 } ]$$

Evaluate

$$\frac{23}{4}=5.75$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$-\frac{3}{4}\left(-8-\left(-\frac{2}{3}\right)-\frac{1}{3}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$-\frac{3}{4}\left(-8+\frac{2}{3}-\frac{1}{3}\right)$$

Convert -8 to fraction -\frac{24}{3}.

$$-\frac{3}{4}\left(-\frac{24}{3}+\frac{2}{3}-\frac{1}{3}\right)$$

Since -\frac{24}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$-\frac{3}{4}\left(\frac{-24+2}{3}-\frac{1}{3}\right)$$

Add -24 and 2 to get -22.

$$-\frac{3}{4}\left(-\frac{22}{3}-\frac{1}{3}\right)$$

Since -\frac{22}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{4}\times \frac{-22-1}{3}$$

Subtract 1 from -22 to get -23.

$$-\frac{3}{4}\left(-\frac{23}{3}\right)$$

Multiply -\frac{3}{4} times -\frac{23}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-23\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{-3\left(-23\right)}{4\times 3}.

$$\frac{69}{12}$$

Reduce the fraction \frac{69}{12} to lowest terms by extracting and canceling out 3.

$$\frac{23}{4}$$

Factor

$$\frac{23}{2 ^ {2}} = 5\frac{3}{4} = 5.75$$