Answer
$a^{7}b^{5}$
Work Step by Step
Using $(ab)^x=a^xb^x$, then the given expression, $
(a^3b)(ab)^4
$, simplifies to
\begin{array}{l}\require{cancel}
(a^3b)(a^4b^4)
.\end{array}
Using $a^x\cdot a^y=a^{x+y}$, then given expression, $
(a^3b)(a^4b^4)
$, simplifies to
\begin{array}{l}\require{cancel}
a^{3+4}b^{1+4}
\\\\=
a^{7}b^{5}
.\end{array}