The problem asks us to simplify the expression $\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}$ and express the answer with positive exponents.

1. Problem Description

The problem asks us to simplify the expression $\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}$ and express the answer with positive exponents.

2. Solution Steps

To simplify the expression $\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}$, we can use the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$. In this case, $a=x$, $m=\frac{4}{5}$, and $n=\frac{3}{5}$.

Applying the quotient rule, we have:

$\frac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}} = x^{\frac{4}{5} - \frac{3}{5}}$

Now, we subtract the exponents:

$\frac{4}{5} - \frac{3}{5} = \frac{4-3}{5} = \frac{1}{5}$

Therefore, the simplified expression is:

$x^{\frac{1}{5}}$

The exponent is positive, so we don't need to do any further manipulation.

3. Final Answer

$x^{\frac{1}{5}}$