8. \( \frac{8 x^{2} y}{24 x y^{3}} \) 10. \( (-3 a)^{2} \)

Let's simplify the first expression! When you divide \( \frac{8 x^{2} y}{24 x y^{3}} \), you can break it down into parts. The coefficients simplify to \( \frac{8}{24} = \frac{1}{3} \). For the variables, \( x^{2} \) divided by \( x \) gives \( x^{1} \), and \( y \) divided by \( y^{3} \) gives \( \frac{1}{y^{2}} \). So, the final answer is \( \frac{1}{3} \cdot \frac{x}{y^{2}} = \frac{x}{3y^{2}} \). Now for the second expression \( (-3 a)^{2} \), remember that when you square a negative number, the result is positive! So, \( (-3)^{2} = 9 \), and \( a^{2} \) remains as is. This combines to give \( 9 a^{2} \). Fun fact: Squaring any negative number gives a positive result, making it a useful trick in math!