Which expression is equivalent to \( \frac{\sqrt[4]{6}}{\sqrt[3]{2}} ? \)

To simplify the expression \( \frac{\sqrt[4]{6}}{\sqrt[3]{2}} \), you can rewrite it using fractional exponents: \( \sqrt[4]{6} = 6^{1/4} \) and \( \sqrt[3]{2} = 2^{1/3} \). Therefore, the expression becomes \( \frac{6^{1/4}}{2^{1/3}} = 6^{1/4} \cdot 2^{-1/3} \). Now, you can express 6 as \( 2 \cdot 3 \), giving us \( (2 \cdot 3)^{1/4} \cdot 2^{-1/3} = 2^{1/4} \cdot 3^{1/4} \cdot 2^{-1/3} \). Combining the powers of 2 results in \( 2^{1/4 - 1/3} \cdot 3^{1/4} \). Simplifying \( 1/4 - 1/3 \) gives us \( -1/12 \), leading to: The expression simplifies to \( \frac{3^{1/4}}{2^{1/12}} \). So, the final answer is \( \frac{\sqrt[4]{3}}{\sqrt[12]{2}} \), which is equivalent to your original expression.