Answer
$27x^{2/3}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
\dfrac{(3x^{1/4})^{3}}{x^{1/12}}
\\\\=
\dfrac{3^3x^{\frac{1}{4}\cdot3}}{x^{\frac{1}{12}}}
\\\\=
\dfrac{27x^{\frac{3}{4}}}{x^{\frac{1}{12}}}
\\\\=
27x^{\frac{3}{4}-\frac{1}{12}}
\\\\=
27x^{\frac{9}{12}-\frac{1}{12}}
\\\\=
27x^{\frac{8}{12}}
\\\\=
27x^{2/3}
.\end{array}
