Divide. Assume that no denominator equals zero. \( \frac{25 n^{12} p^{5}}{5 n^{3} p^{2}} \) \( \begin{array}{ll}\text { a. } 5 n^{-9} p^{-3} & \text { c. } 5 n^{9} p^{3} \\ \text { b. } 5 n^{15} p^{7} & \text { d. } 5 n^{36} p^{10}\end{array} \)

To divide the expression \( \frac{25 n^{12} p^{5}}{5 n^{3} p^{2}} \), we simplify it by dividing the coefficients and using the laws of exponents. Step 1: Divide the coefficients: \( \frac{25}{5} = 5 \). Step 2: For the \( n \) terms, use \( n^{12} \div n^{3} = n^{12-3} = n^{9} \). Step 3: For the \( p \) terms, use \( p^{5} \div p^{2} = p^{5-2} = p^{3} \). Putting it all together, we have: \[ 5 n^{9} p^{3} \] So, the answer is \( \text{c. } 5 n^{9} p^{3} \). --- The laws of exponents can be applied here to express divisions in a concise manner! Remember, when dividing like bases, you subtract the exponents. This principle not only applies to variables but also to numbers—just like when you divide fractions in math! If you're looking for more practice, there are plenty of math resources online that offer interactive problems. Websites like Khan Academy or math-focused YouTube channels can offer videos and quizzes—a fun way to hone your skills while keeping it lighthearted!