Answer
$\dfrac{2b^{9}}{a^{13}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{6a^{-5}b}{3a^8b^{-8}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{3}\cdot2a^{-5-8}b^{1-(-8)}}{\cancel{3}}
\\\\=
2a^{-13}b^{9}
\\\\=
\dfrac{2b^{9}}{a^{13}}
.\end{array}
