1. **State the problem:** Simplify the expression $$\frac{x^{4/5}}{x^{1/5}}$$. 2. **Recall the rule for division of exponents 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:** $$\frac{x^{4/5}}{x^{1/5}} = x^{4/5 - 1/5}$$. 4. **Simplify the exponent:** $$4/5 - 1/5 = 3/5$$. 5. **Final simplified expression:** $$x^{3/5}$$. This means the original expression simplifies to $x^{3/5}$, which is the same as the fifth root of $x$ cubed.