Answer
$\dfrac{b+a^3}{ab}$
Work Step by Step
The given expression, $
\dfrac{a^{-3}+b^{-1}}{a^{-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{a^3}+\dfrac{1}{b^1}}{\dfrac{1}{a^2}}
\\\\=
\dfrac{\dfrac{b+a^3}{a^3b}}{\dfrac{1}{a^2}}
\\\\=
\dfrac{b+a^3}{a^3b}\div\dfrac{1}{a^2}
\\\\=
\dfrac{b+a^3}{a^3b}\cdot a^2
\\\\=
\dfrac{b+a^3}{\cancel{a^2}\cdot ab}\cdot \cancel{a^2}
\\\\=
\dfrac{b+a^3}{ab}
.\end{array}
