Answer
$4t^{-4} \left( t^{2}+2 \right)$
Work Step by Step
Factoring the given factor, $
4t^{-4}
,$ then the given expression, $
4t^{-2}+8t^{-4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
4t^{-4} \left( \dfrac{4t^{-2}}{4t^{-4}}+\dfrac{8t^{-4}}{4t^{-4}} \right)
\\\\=
4t^{-4} \left( t^{-2-(-4)}+2t^{-4-(-4)} \right)
\\\\=
4t^{-4} \left( t^{-2+4}+2t^{-4+4} \right)
\\\\=
4t^{-4} \left( t^{2}+2t^{0} \right)
\\\\=
4t^{-4} \left( t^{2}+2(1) \right)
\\\\=
4t^{-4} \left( t^{2}+2 \right)
.\end{array}
