1. **State the problem:** Simplify the function $f(x) = \frac{3x^4}{x^3}$. 2. **Recall the exponent rule:** When dividing powers with the same base, subtract the exponents: $$\frac{x^a}{x^b} = x^{a-b}$$. 3. **Apply the rule:** $$f(x) = 3 \cdot \frac{x^4}{x^3} = 3x^{4-3} = 3x^1 = 3x$$. 4. **Final answer:** The simplified form of the function is $$f(x) = 3x$$. Note: The second part of your message appears to be a symbolic expression involving sums and variables $a$, $b$, $c$, but it is not a clear question or problem to solve. Therefore, only the first problem is addressed here.