Solve (1/2+3/4)^-1-sqrt[3]{-8}*(-3/2)+(-2)^-2+(-4)^-1

$$( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) ^ { - 1 } - \sqrt[ 3 ] { - 8 } \cdot ( - \frac { 3 } { 2 } ) + ( - 2 ) ^ { - 2 } + ( - 4 ) ^ { - 1 }$$

Evaluate

$$-\frac{11}{5}=-2.2$$

Solution Steps

Add \frac{1}{2} and \frac{3}{4} to get \frac{5}{4}.

$$\left(\frac{5}{4}\right)^{-1}-\sqrt[3]{-8}\left(-\frac{3}{2}\right)+\left(-2\right)^{-2}+\left(-4\right)^{-1}$$

Calculate \frac{5}{4} to the power of -1 and get \frac{4}{5}.

$$\frac{4}{5}-\sqrt[3]{-8}\left(-\frac{3}{2}\right)+\left(-2\right)^{-2}+\left(-4\right)^{-1}$$

Calculate \sqrt[3]{-8} and get -2.

$$\frac{4}{5}-\left(-2\left(-\frac{3}{2}\right)\right)+\left(-2\right)^{-2}+\left(-4\right)^{-1}$$

Multiply -2 and -\frac{3}{2} to get 3.

$$\frac{4}{5}-3+\left(-2\right)^{-2}+\left(-4\right)^{-1}$$

Subtract 3 from \frac{4}{5} to get -\frac{11}{5}.

$$-\frac{11}{5}+\left(-2\right)^{-2}+\left(-4\right)^{-1}$$

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

$$-\frac{11}{5}+\frac{1}{4}+\left(-4\right)^{-1}$$

Add -\frac{11}{5} and \frac{1}{4} to get -\frac{39}{20}.

$$-\frac{39}{20}+\left(-4\right)^{-1}$$

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

$$-\frac{39}{20}-\frac{1}{4}$$

Subtract \frac{1}{4} from -\frac{39}{20} to get -\frac{11}{5}.

$$-\frac{11}{5}$$

Factor

$$-\frac{11}{5} = -2\frac{1}{5} = -2.2$$