[tex] \dfrac{\sqrt[4]6}{\sqrt[3]2}=6^\frac{1}{4}:2^\frac{1}{3}=6^\frac{1\cdot3}{4\cdot3}:2^{\frac{1\cdot4}{3\cdot4}}=6^\frac{3}{12}:2^\frac{4}{12}=(6^3)^\frac{1}{12}:(2^4)^\frac{1}{12}\\\\=216^\frac{1}{12}:16^\frac{1}{12}=(216:16)^\frac{1}{12}=\sqrt[12]{\dfrac{216}{16}}=\sqrt[12]{\dfrac{27}{2}}\\\\\text{Answer:}\ 1)\ \sqrt[12]{\dfrac{27}{2}} [/tex]
