The problem is to simplify the expression $(\frac{x^{1/7}}{y^{4/8}})(\frac{x^{4/7}}{y^{3/3}})$. The answer should be expressed with positive exponents.

1. Problem Description

The problem is to simplify the expression $(\frac{x^{1/7}}{y^{4/8}})(\frac{x^{4/7}}{y^{3/3}})$. The answer should be expressed with positive exponents.

2. Solution Steps

First, we simplify the exponents: $4/8 = 1/2$ and $3/3 = 1$. Then the expression becomes $(\frac{x^{1/7}}{y^{1/2}})(\frac{x^{4/7}}{y^{1}})$.

Next, we multiply the terms with the same base by adding the exponents:

$x^{1/7} * x^{4/7} = x^{(1/7)+(4/7)} = x^{5/7}$

$y^{1/2} * y^{1} = y^{(1/2)+1} = y^{3/2}$

Therefore, the expression becomes $\frac{x^{5/7}}{y^{1/2}y^1} = \frac{x^{5/7}}{y^{3/2}}$.

3. Final Answer

The final answer is $\frac{x^{5/7}}{y^{3/2}}$.