$ \frac{\sqrt[3]{3}}{\sqrt[3]{4}} =\frac{\sqrt[3]{3} \times \sqrt[3]{16}}{4} = \frac{\sqrt[3]{48}}{4} = \frac{\sqrt[3]{8\times 6}}{4} = \frac{2\sqrt[3]{6}}{4}= \frac{1}{2}\sqrt[3]{6} $