Answer
$ab^{3}$
Work Step by Step
$\frac{\sqrt[4] (a^{6}b^{13})}{\sqrt[4] (a^{2}b)}=\sqrt[4] \frac{(a^{6}b^{13})}{(a^{2}b)}=\sqrt (a^{4}b^{12})=\sqrt[4] (a^{4})\times\sqrt[4] (b^{12})=ab^{3}$
We know that $\sqrt[4] (a^{4})=a$, because $(a)^{4}=a^{4}$.
We also know that $\sqrt[4] (b^{12})=b^{3}$, because $(b^{3})^{4}=b^{3\times4}=b^{12}$.
