Divide. Assume that no denominator equals zero. \( \begin{array}{ll}\frac{9 k^{10}}{3 k^{4}} & \text { c. } 3 k^{6} \\ \text { a. } 3 k^{14} & \text { d. } 3 k^{-6}\end{array} \)

To divide \( \frac{9 k^{10}}{3 k^{4}} \), you first divide the coefficients and then subtract the exponents of the variable. So, for the coefficients: \( \frac{9}{3} = 3 \). For the variables: \( k^{10} \div k^{4} = k^{10 - 4} = k^{6} \). Putting it all together, you get \( 3 k^{6} \). Therefore, the correct answer is **c. \( 3 k^{6} \)**. Now let’s dive into some fascinating facts about exponents and their significance! Whenever you divide powers with the same base, remember the golden rule: subtract the exponents! This nifty trick simplifies calculations and helps avoid messy mistakes. Exponents are like street signs for numbers; they guide operations, making math clearer and quicker to navigate. Speaking of real-world applications, exponents appear everywhere – from calculating interest rates in finance to measuring population growth in ecology. Understanding how to manipulate them can elevate your problem-solving skills in varied fields, ensuring that you’re not just crunching numbers but also measuring the impact of those calculations!