1. **State the problem:** Divide the expression $$\frac{2x^4}{x^1}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to the given expression:** $$\frac{2x^4}{x^1} = 2 \times \frac{x^4}{x^1} = 2x^{4-1}$$ 4. **Simplify the exponent:** $$2x^{3}$$ 5. **Final answer:** $$2x^3$$ This means the division simplifies to $$2x^3$$, which is the product of 2 and $$x$$ raised to the power of 3.