#### Answer

$12xy^4\sqrt{xy}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{144x^3y^9}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{144x^2y^8\cdot xy}
\\\\=
\sqrt{(12xy^4)^2\cdot xy}
\\\\=
12xy^4\sqrt{xy}
.\end{array}