Solve (-2)^3*(-1)^4-|-12|div[-(-1/2)^2]

$$( - 2 ) ^ { 3 } \times ( - 1 ) ^ { 4 } - | - 12 | \div [ - ( - \frac { 1 } { 2 } ) ^ { 2 } ]$$

Evaluate

$$40$$

Solution Steps

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

$$-8\left(-1\right)^{4}-\frac{|-12|}{-\left(-\frac{1}{2}\right)^{2}}$$

Calculate -1 to the power of 4 and get 1.

$$-8-\frac{|-12|}{-\left(-\frac{1}{2}\right)^{2}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -12 is 12.

$$-8-\frac{12}{-\left(-\frac{1}{2}\right)^{2}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-8-\frac{12}{-\frac{1}{4}}$$

Divide 12 by -\frac{1}{4} by multiplying 12 by the reciprocal of -\frac{1}{4}.

$$-8-12\left(-4\right)$$

Multiply 12 and -4 to get -48.

$$-8-\left(-48\right)$$

The opposite of -48 is 48.

$$-8+48$$

Add -8 and 48 to get 40.

$$40$$

Factor

$$2^{3}\times 5$$