Solve [-2/5:(-4)]:{[-(2/5+1/2)]:(-9/4)}-frac{(-2)^-2:sqrt[3]{-frac{1}{8}}}{(-frac{1}{2})^4*(-frac{1}{2})^-3}

$$[ - \frac { 2 } { 5 } : ( - 4 ) ] : \{ [ - ( \frac { 2 } { 5 } + \frac { 1 } { 2 } ) ] : ( - \frac { 9 } { 4 } ) \} - \frac { ( - 2 ) ^ { - 2 } : \sqrt[ 3 ] { - \frac { 1 } { 8 } } } { ( - \frac { 1 } { 2 } ) ^ { 4 } \cdot ( - \frac { 1 } { 2 } ) ^ { - 3 } }$$

Evaluate

$$-\frac{3}{4}=-0.75$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$\frac{\frac{-\frac{2}{5}}{-4}}{\frac{-\left(\frac{2}{5}+\frac{1}{2}\right)}{-\frac{9}{4}}}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Divide \frac{-\frac{2}{5}}{-4} by \frac{-\left(\frac{2}{5}+\frac{1}{2}\right)}{-\frac{9}{4}} by multiplying \frac{-\frac{2}{5}}{-4} by the reciprocal of \frac{-\left(\frac{2}{5}+\frac{1}{2}\right)}{-\frac{9}{4}}.

$$\frac{-\frac{2}{5}\left(-\frac{9}{4}\right)}{-4\left(-\left(\frac{2}{5}+\frac{1}{2}\right)\right)}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Multiply -\frac{2}{5} and -\frac{9}{4} to get \frac{9}{10}.

$$\frac{\frac{9}{10}}{-4\left(-\left(\frac{2}{5}+\frac{1}{2}\right)\right)}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Add \frac{2}{5} and \frac{1}{2} to get \frac{9}{10}.

$$\frac{\frac{9}{10}}{-4\left(-\frac{9}{10}\right)}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Multiply -4 and -\frac{9}{10} to get \frac{18}{5}.

$$\frac{\frac{9}{10}}{\frac{18}{5}}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Divide \frac{9}{10} by \frac{18}{5} by multiplying \frac{9}{10} by the reciprocal of \frac{18}{5}.

$$\frac{9}{10}\times \frac{5}{18}-\frac{\frac{\left(-2\right)^{-2}}{\sqrt[3]{-\frac{1}{8}}}}{\left(-\frac{1}{2}\right)^{1}}$$

Multiply \frac{9}{10} and \frac{5}{18} to get \frac{1}{4}.

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

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

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

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

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

Divide \frac{1}{4} by -\frac{1}{2} by multiplying \frac{1}{4} by the reciprocal of -\frac{1}{2}.

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

Multiply \frac{1}{4} and -2 to get -\frac{1}{2}.

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

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

$$\frac{1}{4}-\frac{-\frac{1}{2}}{-\frac{1}{2}}$$

Divide -\frac{1}{2} by -\frac{1}{2} to get 1.

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

Subtract 1 from \frac{1}{4} to get -\frac{3}{4}.

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

Factor

$$-\frac{3}{4} = -0.75$$