Solve (-2)^3-|-1/2|+(1/3)^-2div(3-pi)^0

$$( - 2 ) ^ { 3 } - | - \frac { 1 } { 2 } | + ( \frac { 1 } { 3 } ) ^ { - 2 } \div ( 3 - \pi ) ^ { 0 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Short Solution Steps

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

$$-8-|-\frac{1}{2}|+\frac{\left(\frac{1}{3}\right)^{-2}}{\left(3-\pi \right)^{0}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$-8-\frac{1}{2}+\frac{\left(\frac{1}{3}\right)^{-2}}{\left(3-\pi \right)^{0}}$$

Subtract \frac{1}{2} from -8 to get -\frac{17}{2}.

$$-\frac{17}{2}+\frac{\left(\frac{1}{3}\right)^{-2}}{\left(3-\pi \right)^{0}}$$

Calculate \frac{1}{3} to the power of -2 and get 9.

$$-\frac{17}{2}+\frac{9}{\left(3-\pi \right)^{0}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and \left(3-\pi \right)^{0} is 2. Multiply \frac{9}{\left(3-\pi \right)^{0}} times \frac{2}{2}.

$$-\frac{17}{2}+\frac{9\times 2}{2}$$

Since -\frac{17}{2} and \frac{9\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-17+9\times 2}{2}$$

Do the multiplications in -17+9\times 2.

$$\frac{-17+18}{2}$$

Do the calculations in -17+18.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$