Solve [5-1/3]-[-10-(-2)^3/3]

$$[ 5 - \frac { 1 } { 3 } ] - [ - 10 - \frac { ( - 2 ) ^ { 3 } } { 3 } ]$$

Evaluate

$$12$$

Solution Steps

Convert 5 to fraction \frac{15}{3}.

$$\frac{15}{3}-\frac{1}{3}-\left(-10-\frac{\left(-2\right)^{3}}{3}\right)$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-1}{3}-\left(-10-\frac{\left(-2\right)^{3}}{3}\right)$$

Subtract 1 from 15 to get 14.

$$\frac{14}{3}-\left(-10-\frac{\left(-2\right)^{3}}{3}\right)$$

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

$$\frac{14}{3}-\left(-10-\frac{-8}{3}\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{14}{3}-\left(-10-\left(-\frac{8}{3}\right)\right)$$

The opposite of -\frac{8}{3} is \frac{8}{3}.

$$\frac{14}{3}-\left(-10+\frac{8}{3}\right)$$

Convert -10 to fraction -\frac{30}{3}.

$$\frac{14}{3}-\left(-\frac{30}{3}+\frac{8}{3}\right)$$

Since -\frac{30}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

$$\frac{14}{3}-\frac{-30+8}{3}$$

Add -30 and 8 to get -22.

$$\frac{14}{3}-\left(-\frac{22}{3}\right)$$

The opposite of -\frac{22}{3} is \frac{22}{3}.

$$\frac{14}{3}+\frac{22}{3}$$

Since \frac{14}{3} and \frac{22}{3} have the same denominator, add them by adding their numerators.

$$\frac{14+22}{3}$$

Add 14 and 22 to get 36.

$$\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$