Answer
$2a^{2}b^{3}$
Work Step by Step
$\sqrt [3](8a^{6}b^{9})=\sqrt[3] (8\times a^{6} \times b^{9})=\sqrt[3] 8\times \sqrt[3] (a^{6})\times \sqrt [3](b^{9})=2a^{2}b^{3}$
We know that $\sqrt[3] 8=2$, because $2^{3}=8$. We also know that $\sqrt[3] (a^{6})=a^{2}$, because $(a^{2})^{3}=a^{2\times3}=a^{6}$ and that $\sqrt[3] (b^{9})=b^{3}$, because $(b^{3})^{3}=b^{3\times3}=b^{9}$.
