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 using the exponent rule:** $$\frac{f^3}{f^{18}} = f^{3-18} = f^{-15}$$. 5. **Combine the simplified parts:** $$\frac{1}{4} \times f^{-15} = \frac{1}{4f^{15}}$$. 6. **Final answer:** $$\frac{1}{4f^{15}}$$. This is the fully simplified form of the original expression.