Answer
$3a^{2}b^{}\sqrt[4]{ab}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\sqrt[4]{9ab^3}\sqrt[]{3a^4b}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{9ab^3}\cdot\sqrt[2(2)]{3^{1(2)}a^{4(2)}b^{1(2)}}
\\\\=
\sqrt[4]{9ab^3}\cdot\sqrt[4]{3^{2}a^{8}b^{2}}
\\\\=
\sqrt[4]{9ab^3}\cdot\sqrt[4]{9a^{8}b^{2}}
\\\\=
\sqrt[4]{9ab^3(9a^{8}b^{2})}
\\\\=
\sqrt[4]{81a^{1+8}b^{3+2}}
\\\\=
\sqrt[4]{81a^{9}b^{5}}
\\\\=
\sqrt[4]{81a^{8}b^{4}\cdot ab}
\\\\=
\sqrt[4]{(3a^{2}b^{})^4\cdot ab}
\\\\=
3a^{2}b^{}\sqrt[4]{ab}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
