_
Using these two conversions:
$\displaystyle 27^{\frac{1}{4}}=(3^3)^{\frac{1}{4}}=3^{\frac{3}{4 }}$
$\displaystyle 6^{\frac{3}{4}}=\sqrt[4]{6^3}=\sqrt[4]{216}=\sqrt[4]{3^3 \cdot 2^3}=(3^{\frac{3}{4}})(2^{\frac{3}{4}})$
It follows that
$\displaystyle \frac{(3^{\frac{3}{4}})(3^{\frac{1}{2}})(3^{\frac{ 3}{4}})(2^{\frac{3}{4}})}{2^{\frac{1}{4}}}$