#### Answer

$24x^3\sqrt[]{5x}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
3\sqrt[]{2x^5}\cdot4\sqrt[]{10x^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
3(4)\sqrt[]{2x^5(10x^2)}
\\\\=
12\sqrt[]{20x^7}
\\\\=
12\sqrt[]{4x^6\cdot5x}
\\\\=
12\sqrt[]{(2x^3)^2\cdot5x}
\\\\=
12(2x^3)\sqrt[]{5x}
\\\\=
24x^3\sqrt[]{5x}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.