Answer
$\dfrac{b^{5}c^{4}}{a^{8}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(a^{-5}b^{7}c^{-2})(a^{-3}b^{-2}c^{6})
$, is equivalent to
\begin{array}{l}\require{cancel}
a^{-5+(-3)}b^{7+(-2)}c^{-2+6}
\\\\=
a^{-8}b^{5}c^{4}
\\\\=
\dfrac{b^{5}c^{4}}{a^{8}}
.\end{array}