Answer
$\sqrt[4] (27 a^{2} b^{3})$
Work Step by Step
The product rule holds that $\sqrt[n] a\times\sqrt[n] b=\sqrt[n] (ab)$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers).
Therefore, $\sqrt[4] ab^{2}\times\sqrt[4] 27ab=\sqrt[4] (ab^{2}\times27ab)=\sqrt[4] (27\times a^{1+1}\times b^{2+1})=\sqrt[4] (27 a^{2} b^{3})$