Answer
$2ab^{2}\sqrt[3]{3a^{2}b}$
Work Step by Step
$\sqrt[3] {24a^{5}b^{7}}$
=$\sqrt[3] {8\times3\times a^{3}\times a^{2}\times b^{6}\times b}$
=$\sqrt[3] {2^{3}\times a^{3}\times b^{6}\times3 \times a^{2}\times b}$
=$\sqrt[3] {2^{3}\times a^{3}\times b^{6}} \times \sqrt[3]{3 \times a^{2}\times b}$
=$2ab^{2}\sqrt[3]{3a^{2}b}$