1. **State the problem:** Calculate the product $9^7 \times 9^8$. 2. **Formula used:** When multiplying powers with the same base, use the rule: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is 9, and the exponents are 7 and 8. $$9^7 \times 9^8 = 9^{7+8}$$ 4. **Simplify the exponent:** $$9^{7+8} = 9^{15}$$ 5. **Final answer:** $$\boxed{9^{15}}$$ This means the product of $9^7$ and $9^8$ is $9^{15}$.