1. **State the problem:** Find the cube root of the expression $$87448p^9r^2$$. 2. **Recall the formula:** The cube root of a product is the product of the cube roots: $$\sqrt[3]{abc} = \sqrt[3]{a} \cdot \sqrt[3]{b} \cdot \sqrt[3]{c}$$. 3. **Apply the cube root to each factor:** $$\sqrt[3]{87448p^9r^2} = \sqrt[3]{87448} \cdot \sqrt[3]{p^9} \cdot \sqrt[3]{r^2}$$ 4. **Simplify each term:** - For $$p^9$$, since $$\sqrt[3]{p^9} = p^{9/3} = p^3$$. - For $$r^2$$, since the exponent 2 is less than 3, it remains inside the root: $$\sqrt[3]{r^2}$$. 5. **Simplify $$\sqrt[3]{87448}$$:** Factor 87448 to find perfect cubes: $$87448 = 2^3 \times 10931$$ (since $$2^3=8$$ and $$87448/8=10931$$). So, $$\sqrt[3]{87448} = \sqrt[3]{2^3 \times 10931} = 2 \cdot \sqrt[3]{10931}$$. 6. **Combine all parts:** $$\sqrt[3]{87448p^9r^2} = 2 \cdot p^3 \cdot \sqrt[3]{10931r^2}$$. **Final answer:** $$\boxed{2p^3\sqrt[3]{10931r^2}}$$