1. **State the problem:** Simplify the expression $$\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing expressions with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule:** $$\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}} = x^{\frac{4}{5} - \frac{3}{5}}$$. 4. **Subtract the exponents:** $$\frac{4}{5} - \frac{3}{5} = \frac{4 - 3}{5} = \frac{1}{5}$$. 5. **Write the simplified expression:** $$x^{\frac{1}{5}}$$. 6. **Interpretation:** This means the fifth root of $x$. **Final answer:** $$x^{\frac{1}{5}}$$