#### Answer

$y\sqrt[]{5y}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{\sqrt[]{40xy^3}}{\sqrt[]{8x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{40xy^3}{8x}}
\\\\=
\sqrt[]{5x^{1-1}y^3}
\\\\=
\sqrt[]{5x^{0}y^3}
\\\\=
\sqrt[]{5y^3}
\\\\=
\sqrt[]{y^2\cdot5y}
\\\\=
\sqrt[]{(y)^2\cdot5y}
\\\\=
y\sqrt[]{5y}
.\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.