1. **State the problem:** Simplify the expression $$\frac{\sqrt[4]{x^9}}{\sqrt[4]{x^2}}$$ using rational exponents. 2. **Rewrite radicals as rational exponents:** Recall that $$\sqrt[n]{x^m} = x^{\frac{m}{n}}$$. So, $$\sqrt[4]{x^9} = x^{\frac{9}{4}}$$ and $$\sqrt[4]{x^2} = x^{\frac{2}{4}} = x^{\frac{1}{2}}$$. 3. **Divide using exponent rules:** When dividing with the same base, subtract exponents: $$\frac{x^{\frac{9}{4}}}{x^{\frac{1}{2}}} = x^{\frac{9}{4} - \frac{1}{2}}$$. 4. **Find common denominator and subtract:** $$\frac{9}{4} - \frac{1}{2} = \frac{9}{4} - \frac{2}{4} = \frac{7}{4}$$. 5. **Final simplified expression:** $$x^{\frac{7}{4}}$$. **Answer:** $$x^{\frac{7}{4}}$$. This matches the choice $x^{7/4}$.