Answer
$\sqrt[6]{144}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\sqrt[]{3}\cdot\sqrt[3]{4}
\\\\=
3^{\frac{1}{2}}\cdot4^{\frac{1}{3}}
\\\\=
3^{\frac{3}{6}}\cdot4^{\frac{2}{6}}
\\\\=
(3^3\cdot4^2)^{\frac{1}{6}}
\\\\=
(9\cdot16)^{\frac{1}{6}}
\\\\=
(144)^{\frac{1}{6}}
\\\\=
\sqrt[6]{144}
.\end{array}
