Solve (-1/2+3/4)^{-1}-sqrt[3]{(1-7/8)^-1}(-1-1/2)+(-2)^2*(-2)^3:(-2)^7=

$$( - \frac { 1 } { 2 } + \frac { 3 } { 4 } ) ^ { - 1 } - \sqrt[ 3 ] { ( 1 - \frac { 7 } { 8 } ) ^ { - 1 } } ( - 1 - \frac { 1 } { 2 } ) + ( - 2 ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } : ( - 2 ) ^ { 7 } =$$

Evaluate

$$\frac{29}{4}=7.25$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-\frac{1}{2}+\frac{3}{4}\right)^{-1}-\sqrt[3]{\left(1-\frac{7}{8}\right)^{-1}}\left(-1-\frac{1}{2}\right)+\frac{\left(-2\right)^{5}}{\left(-2\right)^{7}}$$

Rewrite \left(-2\right)^{7} as \left(-2\right)^{5}\left(-2\right)^{2}. Cancel out \left(-2\right)^{5} in both numerator and denominator.

$$\left(-\frac{1}{2}+\frac{3}{4}\right)^{-1}-\sqrt[3]{\left(1-\frac{7}{8}\right)^{-1}}\left(-1-\frac{1}{2}\right)+\frac{1}{\left(-2\right)^{2}}$$

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

$$\left(\frac{1}{4}\right)^{-1}-\sqrt[3]{\left(1-\frac{7}{8}\right)^{-1}}\left(-1-\frac{1}{2}\right)+\frac{1}{\left(-2\right)^{2}}$$

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

$$4-\sqrt[3]{\left(1-\frac{7}{8}\right)^{-1}}\left(-1-\frac{1}{2}\right)+\frac{1}{\left(-2\right)^{2}}$$

Subtract \frac{7}{8} from 1 to get \frac{1}{8}.

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

Calculate \frac{1}{8} to the power of -1 and get 8.

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

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

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

Subtract \frac{1}{2} from -1 to get -\frac{3}{2}.

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

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

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

The opposite of -3 is 3.

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

Add 4 and 3 to get 7.

$$7+\frac{1}{\left(-2\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$7+\frac{1}{4}$$

Add 7 and \frac{1}{4} to get \frac{29}{4}.

$$\frac{29}{4}$$

Factor

$$\frac{29}{2 ^ {2}} = 7\frac{1}{4} = 7.25$$