Solve (3(-2)^2/2-(-2)^3/3-(-2)^2/2-2^2)

$$( \frac { 3 ( - 2 ) ^ { 2 } } { 2 } - \frac { ( - 2 ) ^ { 3 } } { 3 } \frac { - ( - 2 ) ^ { 2 } } { 2 } - 2 ^ { 2 } )$$

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\frac{12}{2}-\frac{\left(-2\right)^{3}}{3}\times \frac{-\left(-2\right)^{2}}{2}-2^{2}$$

Divide 12 by 2 to get 6.

$$6-\frac{\left(-2\right)^{3}}{3}\times \frac{-\left(-2\right)^{2}}{2}-2^{2}$$

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

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

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

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

Calculate -2 to the power of 2 and get 4.

$$6-\left(-\frac{8}{3}\times \frac{-4}{2}\right)-2^{2}$$

Divide -4 by 2 to get -2.

$$6-\left(-\frac{8}{3}\left(-2\right)\right)-2^{2}$$

Express -\frac{8}{3}\left(-2\right) as a single fraction.

$$6-\frac{-8\left(-2\right)}{3}-2^{2}$$

Multiply -8 and -2 to get 16.

$$6-\frac{16}{3}-2^{2}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{18}{3}-\frac{16}{3}-2^{2}$$

Since \frac{18}{3} and \frac{16}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-16}{3}-2^{2}$$

Subtract 16 from 18 to get 2.

$$\frac{2}{3}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{3}-4$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{2}{3}-\frac{12}{3}$$

Since \frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-12}{3}$$

Subtract 12 from 2 to get -10.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$