Solve -2^2+8div(-2)^3-2*(1/8-1/2)

$$- 2 ^ { 2 } + 8 \div ( - 2 ) ^ { 3 } - 2 \times ( \frac { 1 } { 8 } - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{17}{4}=-4.25$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

Divide 8 by -8 to get -1.

$$-4-1-2\left(\frac{1}{8}-\frac{1}{2}\right)$$

Subtract 1 from -4 to get -5.

$$-5-2\left(\frac{1}{8}-\frac{1}{2}\right)$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

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

Since \frac{1}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$-5-2\times \frac{1-4}{8}$$

Subtract 4 from 1 to get -3.

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

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

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

Multiply 2 and -3 to get -6.

$$-5-\frac{-6}{8}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$-5-\left(-\frac{3}{4}\right)$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$-5+\frac{3}{4}$$

Convert -5 to fraction -\frac{20}{4}.

$$-\frac{20}{4}+\frac{3}{4}$$

Since -\frac{20}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{-20+3}{4}$$

Add -20 and 3 to get -17.

$$-\frac{17}{4}$$

Factor

$$-\frac{17}{4} = -4\frac{1}{4} = -4.25$$