2ху^3/8х^2у^2

To simplify the expression \( \frac{2xy^3}{8x^2y^2} \), you can follow these steps:

1. Factor out any common terms from the numerator and the denominator.
2. Simplify coefficients (numerical values) and the variables separately.

Let's break it down:

1. In the numerator \( 2xy^3 \) and in the denominator \( 8x^2y^2 \):
   • The coefficient \( \frac{2}{8} \) simplifies to \( \frac{1}{4} \).
   • The variable \( x \) in the numerator is \( x^1 \) and \( x^2 \) in the denominator. When simplifying, \( \frac{x^1}{x^2} = \frac{1}{x^{2-1}} = \frac{1}{x} \).
   • The variable \( y^3 \) in the numerator and \( y^2 \) in the denominator can be simplified as \( \frac{y^3}{y^2} = y^{3-2} = y^1 = y \).

Putting it all together:

\[ \frac{2xy^3}{8x^2y^2} = \frac{1}{4} \cdot \frac{1}{x} \cdot y = \frac{y}{4x} \]

So, the simplified expression is:

\[ \frac{y}{4x} \]