1. **Problem:** Simplify the rational expression \(\frac{2x^2 y^5}{3x^3 y^2}\). 2. **Formula and rules:** To simplify a fraction with variables, divide numerator and denominator by their common factors. For powers of the same base, use the rule \(a^m \div a^n = a^{m-n}\). 3. **Step-by-step simplification:** \[\frac{2x^2 y^5}{3x^3 y^2} = \frac{2 \cancel{x^2} y^5}{3 \cancel{x^3} y^2} = \frac{2 y^5}{3 x^{3-2} y^2} = \frac{2 y^5}{3 x^{1} y^2}\] 4. Simplify powers of \(y\): \[\frac{2 y^5}{3 x y^2} = \frac{2 \cancel{y^5}}{3 x \cancel{y^2}} = \frac{2 y^{5-2}}{3 x} = \frac{2 y^3}{3 x}\] 5. **Final answer:** \[\boxed{\frac{2 y^3}{3 x}}\] This is the simplified form of the given rational expression.