1. **State the problem:** Simplify the expression $$\frac{3f^3}{12f^{18}}$$. 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:** $$\frac{3}{12} = \frac{\cancel{3}^1}{\cancel{3}^4} = \frac{1}{4}$$. 4. **Simplify the variables:** $$\frac{f^3}{f^{18}} = f^{3-18} = f^{-15}$$. 5. **Combine the results:** $$\frac{3f^3}{12f^{18}} = \frac{1}{4} f^{-15}$$. 6. **Rewrite with positive exponent:** $$\frac{1}{4} f^{-15} = \frac{1}{4f^{15}}$$. **Final answer:** $$\frac{1}{4f^{15}}$$.