7. Simplify the following expression: \( \frac{3 x^{4} y^{2}}{x y^{2}} \) A. \( 3 x^{3} \) B. \( 3 x^{2} y \) C. \( 3 x^{4} y \) D. \( \frac{3 x^{3} y}{x y} \)

To simplify the expression \( \frac{3 x^{4} y^{2}}{x y^{2}} \), we can cancel the common terms in the numerator and the denominator. The \( y^{2} \) in the numerator and denominator cancels out, leaving us with \( \frac{3 x^{4}}{x} \). Now, simplify \( x^{4} \div x = x^{3} \). Thus, the simplified expression is \( 3 x^{3} \). So, the answer is A. \( 3 x^{3} \). To make simplifying fractions like this even more fun, remember that when writing expressions, you can think of them like reducing a math potion! The fewer ingredients (or terms) you have, the more potent (or simpler) your equation becomes. Always look to cancel what's on both sides first! If you want to dive deeper into powers and exponents, a great resource is "The Joy of x: A Guided Tour of Math, from One to Infinity" by Steven Strogatz. It's a delightful read that brings mathematical concepts to life with real-world applications and stories!