Answer
$2a^{2}b^{3}\sqrt[3] {3a}$
Work Step by Step
$\sqrt[3] {24a^{7}b^{9}}$
=$\sqrt[3] {8\times3\times a^{6}\times a \times b^{9}}$
=$\sqrt[3] {8\times a^{6} \times b^{9}\times3\times a}$
=$\sqrt[3] {2^{3}\times a^{6}\times b^{9}}\times \sqrt[3] {3\times a}$
=$2a^{2}b^{3}\times \sqrt[3] {3\times a}$
=$2a^{2}b^{3}\sqrt[3] {3a}$