Solve |-2^2+(-2)^3-2^-1+(-2)^-2|=

$$| - 2 ^ { 2 } + ( - 2 ) ^ { 3 } - 2 ^ { - 1 } + ( - 2 ) ^ { - 2 } | =$$

Evaluate

$$\frac{49}{4}=12.25$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

Subtract 8 from -4 to get -12.

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

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

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

Subtract \frac{1}{2} from -12 to get -\frac{25}{2}.

$$|-\frac{25}{2}+\left(-2\right)^{-2}|$$

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

$$|-\frac{25}{2}+\frac{1}{4}|$$

Add -\frac{25}{2} and \frac{1}{4} to get -\frac{49}{4}.

$$|-\frac{49}{4}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{49}{4} is \frac{49}{4}.

$$\frac{49}{4}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {2}} = 12\frac{1}{4} = 12.25$$