Solve [(-1/2)^3*(-2^4)/(-2)^2]^-1=?

$$[ \frac { ( - \frac { 1 } { 2 } ) ^ { 3 } \cdot ( - 2 ^ { 4 } ) } { ( - 2 ) ^ { 2 } } ] ^ { - 1 } = ?$$

Evaluate

$$2$$

Solution Steps

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

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

Calculate 2 to the power of 4 and get 16.

$$\left(\frac{-\frac{1}{8}\left(-16\right)}{\left(-2\right)^{2}}\right)^{-1}$$

Multiply -\frac{1}{8} and -16 to get 2.

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

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

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

$$2$$

Factor

$$2$$