Answer
$a^{2}b\sqrt[4] (b^{3})$
Work Step by Step
$\sqrt [4] (a^{8}b^{7})=\sqrt [4] (a^{8}) \times\sqrt[4] (b^{4})\times\sqrt[4] (b^{3})=a^{2}b\sqrt[4] (b^{3})$
We know that $\sqrt [4] (a^{8})=a^{2}$, because $(a^{2})^{4}=a^{2\times4}=a^{8}$. We also know that $\sqrt[4] (b^{4})=b$, because $(b)^{4}=b^{4}$.
