Now let's add more variables or bases: Solve: \( \frac{-18 x^{5} y^{3}}{-6 x^{2} y} \) \( 3 x^{3} y \) \( 3 x^{3} y^{2} \quad \) (don't forget \( y=y^{1)} \) Rewatch

Let's tackle this problem step-by-step for clarity! First, simplify the fraction: \[ \frac{-18 x^{5} y^{3}}{-6 x^{2} y} = \frac{18}{6} \cdot \frac{x^{5}}{x^{2}} \cdot \frac{y^{3}}{y} = 3 x^{3} y^{2} \] Now, our expression simplifies to \( 3 x^{3} y^{2} \). A fun tip for remembering how to simplify algebraic fractions is to think of each variable and its powers as a recipe. The variables are like ingredients and simplifying is just figuring out how to cook them down to their essence! Another great perspective is to consider real-world applications of algebraic manipulation. Many engineers and scientists must simplify expressions regularly to solve real-world problems, such as optimizing materials in construction or calculating forces in mechanics, making these skills not only practical but essential!