1. **State the problem:** Simplify the expression $$\frac{k^4}{4k^3}$$. 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 to the expression:** $$\frac{k^4}{4k^3} = \frac{k^4}{\cancel{4}k^3} = \frac{k^{4-3}}{4} = \frac{k^1}{4}$$ 4. **Simplify the expression:** $$\frac{k}{4}$$ 5. **Final answer:** The simplified form of $$\frac{k^4}{4k^3}$$ is $$\frac{k}{4}$$.