Answer
$-a^{2}b^{3}$
Work Step by Step
$\sqrt[3] (-a^{6}b^{9})=\sqrt[3] (-1\times a^{6}\times b^{9})=\sqrt[3] (-1) \times \sqrt[3] (a^{6})\times \sqrt[3] (b^{9})=-a^{2}b^{3}$
$\sqrt[3] (-1)=-1$, because $(-1)^{3}=-1\times-1\times-1=-1$.
$\sqrt[3] (a^{6})=a^{2}$, because $(a^{2})^{3}=a^{2\times3}=a^{6}$.
$\sqrt[3] (b^{9})=b^{3}$, because $(b^{3})^{3}=b^{3\times3}=b^{9}$.
