1. The problem asks to use the product rule to simplify a radical expression. 2. The product rule for radicals states that $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ for non-negative numbers $a$ and $b$. 3. Since the user did not specify the exact radical expression, let's consider a general example: simplify $$\sqrt{10 \cdot 7}$$. 4. Applying the product rule: $$\sqrt{10 \cdot 7} = \sqrt{10} \cdot \sqrt{7}$$. 5. This expression cannot be simplified further because 10 and 7 have no perfect square factors. 6. Therefore, the simplified form is $$\sqrt{10} \cdot \sqrt{7}$$ or equivalently $$\sqrt{70}$$. 7. Among the options given (10, 7, and two unspecified), the product rule shows the product inside the radical is 70, which is not listed as an option. 8. If the question is to choose between 10 or 7 as simplified parts, the product rule separates the radical into $$\sqrt{10}$$ and $$\sqrt{7}$$. Final answer: The product rule simplifies $$\sqrt{10 \cdot 7}$$ to $$\sqrt{10} \cdot \sqrt{7}$$.