1. The problem is to rewrite the expression $$\sqrt[3]{x^7}$$ using rational exponents. 2. Recall the rule for radicals and exponents: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ where $n$ is the root and $m$ is the power. 3. Applying this rule to our expression, we have: $$\sqrt[3]{x^7} = x^{\frac{7}{3}}$$ 4. This is the expression rewritten with rational exponents. Final answer: $$x^{\frac{7}{3}}$$