#### Answer

$2x^4\sqrt{2x}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt{8x^9}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{4x^8\cdot2x}
\\\\=
\sqrt{(2x^4)^2\cdot2x}
.\\\\=
2x^4\sqrt{2x}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.