1. The problem asks to write the radical expression $$\sqrt[3]{r^4}$$ as an expression with a rational exponent. 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 radical. 3. Applying this rule to $$\sqrt[3]{r^4}$$, we get: $$r^{\frac{4}{3}}$$ 4. This is the expression with a rational exponent equivalent to the original radical. Final answer: $$r^{\frac{4}{3}}$$