Solve (-2)^3-3*[(-4)^2+2]-(-3)^2div(-2)

$$( - 2 ) ^ { 3 } - 3 \times [ ( - 4 ) ^ { 2 } + 2 ] - ( - 3 ) ^ { 2 } \div ( - 2 )$$

Evaluate

$$-\frac{115}{2}=-57.5$$

Solution Steps

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

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

Calculate -4 to the power of 2 and get 16.

$$-8-3\left(16+2\right)-\frac{\left(-3\right)^{2}}{-2}$$

Add 16 and 2 to get 18.

$$-8-3\times 18-\frac{\left(-3\right)^{2}}{-2}$$

Multiply 3 and 18 to get 54.

$$-8-54-\frac{\left(-3\right)^{2}}{-2}$$

Subtract 54 from -8 to get -62.

$$-62-\frac{\left(-3\right)^{2}}{-2}$$

Calculate -3 to the power of 2 and get 9.

$$-62-\frac{9}{-2}$$

Fraction \frac{9}{-2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$-62-\left(-\frac{9}{2}\right)$$

The opposite of -\frac{9}{2} is \frac{9}{2}.

$$-62+\frac{9}{2}$$

Convert -62 to fraction -\frac{124}{2}.

$$-\frac{124}{2}+\frac{9}{2}$$

Since -\frac{124}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{-124+9}{2}$$

Add -124 and 9 to get -115.

$$-\frac{115}{2}$$

Factor

$$-\frac{115}{2} = -57\frac{1}{2} = -57.5$$