1. **State the problem:** Simplify the expression $$\frac{3a^3}{12a^9}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{3}{12} = \frac{1}{4}$$. 4. **Simplify the variables:** $$a^{3-9} = a^{-6}$$. 5. **Combine the results:** $$\frac{1}{4}a^{-6}$$. 6. **Rewrite with positive exponents:** $$\frac{1}{4a^6}$$. **Final answer:** $$\frac{1}{4a^6}$$.