Answer
$2ab^{2}\sqrt[3] (3a^{2}b)$
Work Step by Step
$\sqrt[3] (24a^{5}b^{7})=\sqrt[3] (8\times a^{3}\times b^{6}\times3a^{2}b)=\sqrt[3] 8\times\sqrt[3] (a^{3})\times\sqrt [3] (b^{6})\times\sqrt[3] (3a^{2}b)=2ab^{2}\sqrt[3] (3a^{2}b)$
$\sqrt[3] 8=2$, because $2^{3}=8$
$\sqrt[3] (a^{3})=a$, because $(a)^{3}=a^{3}$
$\sqrt[3] (b^{6})=b^{2}$, because $(b^{3})^{2}=b^{3\times2}=b^{6}$
