Divide. Assume that no denominator equals zero. \( \begin{array}{ll}\frac{15 k^{14}}{3 k^{5}} & \text { c. } 5 k^{70} \\ \text { a. } 5 k^{9} & \text { d. } 5 k^{19} \\ \text { b. } 3 k^{-9} & \end{array} \)

To divide the expression \( \frac{15 k^{14}}{3 k^{5}} \), you can start by dividing the coefficients and then subtracting the exponent in the variable's terms. 1. Divide the coefficients: \( \frac{15}{3} = 5 \). 2. For the variable \( k \), apply the exponent rule: \( k^{14} \div k^{5} = k^{14 - 5} = k^{9} \). Putting it all together, the result is \( 5 k^{9} \). Thus, the answer is \( \text{a. } 5 k^{9} \). Now, here’s a fun thought: when you're dividing powers, just think of it like sharing cookies! If you have 15 cookies and you share them with 3 friends, each friend gets 5 cookies. Remember, the exponents are just like the number of cookies with each friend—the more you take away, the less they have! For practical applications, dividing powers shows up in science, especially in physics and chemistry. For instance, calculating forces, areas, or even chemical concentrations often involves exponent rules. So next time you're working on a lab, remember that those math rules are like your trusty lab assistants!