Solve 1/3*-2^3-5/2*-2^2+4*(-2)-2

$$\frac{ 1 }{ 3 } \times { -2 }^{ 3 } - \frac{ 5 }{ 2 } \times { -2 }^{ 2 } +4 \times (-2)-2$$

Evaluate

$$-\frac{68}{3}\approx -22.666666667$$

Solution Steps

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

$$\frac{1}{3}\left(-8\right)-\frac{5}{2}\left(-2\right)^{2}+4\left(-2\right)-2$$

Multiply \frac{1}{3} and -8 to get \frac{-8}{3}.

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

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

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

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

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

Express \frac{5}{2}\times 4 as a single fraction.

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

Multiply 5 and 4 to get 20.

$$-\frac{8}{3}-\frac{20}{2}+4\left(-2\right)-2$$

Divide 20 by 2 to get 10.

$$-\frac{8}{3}-10+4\left(-2\right)-2$$

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

$$-\frac{8}{3}-\frac{30}{3}+4\left(-2\right)-2$$

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

$$\frac{-8-30}{3}+4\left(-2\right)-2$$

Subtract 30 from -8 to get -38.

$$-\frac{38}{3}+4\left(-2\right)-2$$

Multiply 4 and -2 to get -8.

$$-\frac{38}{3}-8-2$$

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

$$-\frac{38}{3}-\frac{24}{3}-2$$

Since -\frac{38}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-38-24}{3}-2$$

Subtract 24 from -38 to get -62.

$$-\frac{62}{3}-2$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{62}{3}-\frac{6}{3}$$

Since -\frac{62}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-62-6}{3}$$

Subtract 6 from -62 to get -68.

$$-\frac{68}{3}$$

Factor

$$-\frac{68}{3} = -22\frac{2}{3} = -22.666666666666668$$