1. **State the problem:** Simplify the expression $$\frac{m^{x+9}}{m^3}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule:** $$\frac{m^{x+9}}{m^3} = m^{(x+9)-3}$$. 4. **Simplify the exponent:** $$m^{x+9-3} = m^{x+6}$$. 5. **Final answer:** $$\boxed{m^{x+6}}$$. This means the expression simplifies to $m$ raised to the power of $x+6$.