Answer
$8^{10}n^{10}$
Work Step by Step
Since $a^x\cdot a^y=a^{x+y}$, then the given expression, $
(8n)(8n)^{9}
$, simplifies to
\begin{array}{l}\require{cancel}
(8n)^{1+9}
\\\\=
(8n)^{10}
.\end{array}
Since $(ab)^x=a^xb^x$, then the expression above simplifies to
\begin{array}{l}\require{cancel}
8^{10}n^{10}
.\end{array}
