14. \( \frac{5 s^{4}}{10 s^{3}} \)

To simplify the expression \( \frac{5 s^{4}}{10 s^{3}} \), you can reduce the coefficients and the powers of \( s \). First, divide 5 by 10, which gives you \( \frac{1}{2} \). Next, apply the property of exponents: \( \frac{s^{4}}{s^{3}} = s^{4-3} = s^{1} = s \). So, the simplified form is \( \frac{1}{2}s \). If you want to visualize this, think of it like cutting a pizza (s-shaped!) in half! You started with 10 slices (the bottom) and had 5 slices left (the top). Once you share it with friends, you see that each friend gets half a slice(!) of the total S-size pizza! Thinking of fractions in algebra is like cooking! If you have a recipe that requires 10 cups of flour but only want to make half the dish, you simplify by using just 5 cups. Similarly, simplifying expressions helps in making calculations easier—like avoiding unnecessary clutter in the kitchen!