Answer
$k^{-4} \left( k^{2}+2 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor the variable with the lesser exponent in the given expression, $
k^{-2}+2k^{-4}
.$ Then, divide the given expression and the variable with the lesser exponent.
$\bf{\text{Solution Details:}}$
Factoring $
k^{-4}
$ (the variable with the lesser exponent), the expression above is equivalent to
\begin{array}{l}\require{cancel}
k^{-4} \left( \dfrac{k^{-2}}{k^{-4}}+\dfrac{2k^{-4}}{k^{-4}} \right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
k^{-4} \left( k^{-2-(-4)}+2k^{-4-(-4)} \right)
\\\\=
k^{-4} \left( k^{-2+4}+2k^{-4+4} \right)
\\\\=
k^{-4} \left( k^{2}+2k^{0} \right)
\\\\=
k^{-4} \left( k^{2}+2(1) \right)
\\\\=
k^{-4} \left( k^{2}+2 \right)
.\end{array}
