Answer
$126ab^2c^5$
Work Step by Step
Using $x^a\cdot x^b=x^{a+b}$, the given expression, $
(9abc^3)(14bc^2)
,$ simplifies to
\begin{array}{l}\require{cancel}
(9)(14)a^{}b^{1+1}c^{3+2}
\\\\=
126ab^2c^5
.\end{array}
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