12) \( \frac{5 x y^{2}}{5 y^{3}} \)

To simplify the expression \( \frac{5 x y^{2}}{5 y^{3}} \), you start by canceling the common factors in the numerator and the denominator. The 5s in both the numerator and denominator cancel out, which gives you \( \frac{x y^{2}}{y^{3}} \). You can then simplify further by subtracting the exponents of \( y \). This results in \( \frac{x}{y} \), since \( y^{2-3} = y^{-1} \), and can be written as \( x y^{-1} \) or \( \frac{x}{y} \). To double-check, plug in a few values for \( x \) and \( y \). For example, if \( x = 1 \) and \( y = 2 \), the original expression yields \( \frac{5 \cdot 1 \cdot 2^2}{5 \cdot 2^3} = \frac{20}{40} = \frac{1}{2} \). Using the simplified version \( \frac{x}{y} \) gives \( \frac{1}{2} \) too, confirming the simplification is correct!