1. **Problem:** Simplify the expression $6^7 \cdot 6^9$ and verify if it equals $6^{16}$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** $$6^7 \cdot 6^9 = 6^{7+9} = 6^{16}$$ 4. **Explanation:** Since the bases are the same (6), we add the exponents 7 and 9 to get 16. 5. **Final answer:** $$6^7 \cdot 6^9 = 6^{16}$$