2ху^3/8х^2у^2

To simplify the expression \(\frac{2xy^3}{8x^2y^2}\), we can start by simplifying the coefficients and the variables separately.

1. Coefficients:

   • The coefficient \(2\) in the numerator and \(8\) in the denominator can be simplified: \[ \frac{2}{8} = \frac{1}{4} \]

2. Variables:

   • For the variable \(x\): \[ x^1 \text{ (in the numerator)} \text{ and } x^2 \text{ (in the denominator)} \rightarrow x^{1-2} = x^{-1} = \frac{1}{x} \]
   • For the variable \(y\): \[ y^3 \text{ (in the numerator)} \text{ and } y^2 \text{ (in the denominator)} \rightarrow y^{3-2} = y^1 = y \]

Putting it all together, we have: \[ \frac{2xy^3}{8x^2y^2} = \frac{1}{4} \cdot \frac{y}{x} \]

So the simplified expression is: \[ \frac{y}{4x} \]