Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{{(-\frac{1}{2})}^{3}}{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
Since the power of 3 is odd, the result will be negative.
\[\begin{aligned}&\frac{1}{-{(\frac{1}{2})}^{3}}{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\begin{aligned}&\frac{1}{-\frac{1}{{2}^{3}}}{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
Simplify \({2}^{3}\) to \(8\).
\[\begin{aligned}&\frac{1}{-\frac{1}{8}}{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
Move the negative sign to the left.
\[\begin{aligned}&-\frac{1}{\frac{1}{8}}{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&-8{(\frac{1}{2})}^{-k}\\&{(\frac{1}{2})}^{-5}\end{aligned}\]
-8*(1/2)^-k;(1/2)^-5
