Answer
$2ab^{2}$
Work Step by Step
$\sqrt[5] (32a^{5}b^{10})=\sqrt[5] (32\times a^{5}\times b^{10})=\sqrt[5] 32\times\sqrt[5] (a^{5})\times\sqrt[5] (b^{10})=2ab^{2}$
$\sqrt[5] 32=2$, because $2^{5}=32$
$\sqrt[5] (a^{5})=a$, because $(a)^{5}=a^{5}$
$\sqrt[5] (b^{10})=b^{2}$, because $(b^{2})^{5}=b^{2\times5}=b^{10}$
