Answer
$k^{-2} \left( 4k^{}+1 \right)$
Work Step by Step
Factoring the given factor, $
k^{-2}
,$ then the given expression, $
4k^{-1}+k^{-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
k^{-2} \left( \dfrac{4k^{-1}}{k^{-2}}+\dfrac{k^{-2}}{k^{-2}} \right)
\\\\=
k^{-2} \left( 4k^{-1-(-2)}+k^{-2-(-2)} \right)
\\\\=
k^{-2} \left( 4k^{-1+2}+k^{-2+2} \right)
\\\\=
k^{-2} \left( 4k^{1}+k^{0} \right)
\\\\=
k^{-2} \left( 4k^{}+1 \right)
.\end{array}
