1. The problem asks to write the expression $$\sqrt[3]{x^5} + \sqrt[4]{y^2}$$ in terms of rational exponents. 2. Recall the rule for converting radicals to rational exponents: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ where $n$ is the root and $m$ is the power inside the root. 3. Apply this rule to each term: - For $$\sqrt[3]{x^5}$$, we have $$x^{\frac{5}{3}}$$. - For $$\sqrt[4]{y^2}$$, we have $$y^{\frac{2}{4}}$$. 4. Simplify the exponent $$\frac{2}{4}$$ to $$\frac{1}{2}$$, so the second term becomes $$y^{\frac{1}{2}}$$. 5. Therefore, the expression in rational exponents is: $$x^{\frac{5}{3}} + y^{\frac{1}{2}}$$ 6. Among the given options, the correct one is $$x^{\frac{5}{3}} + y^{\frac{1}{2}}$$. This matches the third option in the list. Final answer: $$x^{\frac{5}{3}} + y^{\frac{1}{2}}$$