Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 97

$2y^{2}\sqrt[3]{y}$

$\displaystyle \frac{\sqrt[3]{24xy^{8}}}{\sqrt[3]{3xy}}=\sqrt[3]{\frac{24xy^{8}}{3xy}}=\qquad $... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ $=\sqrt[3]{8y^{7}}$ $=\sqrt[3]{2^{3}\cdot y^{6}\cdot y}$ $=\sqrt[3]{2^{3}}\cdot\sqrt[3]{y^{6}}\cdot\sqrt[3]{y}$ $=2y^{2}\sqrt[3]{y}$