c) \( b^{5 n}: b^{n-2} \)

To simplify the expression \( \frac{b^{5n}}{b^{n-2}} \), we can use the property of exponents which states that when you divide like bases, you subtract their exponents. This gives us: \[ b^{5n - (n-2)} = b^{5n - n + 2} = b^{4n + 2} \] So the simplified form of the expression is \( b^{4n + 2} \). To explore further, it's interesting to note the role of exponents in various fields, such as computer science, where they help in analyzing algorithms' time complexity. For example, an algorithm with a complexity of \( O(n^2) \) will take exponentially more time as \( n \) increases, demonstrating how critical exponent rules are in practical coding scenarios. Also, you might want to brush up on the laws of exponents if you haven't already, as they're foundational in mathematics and sciences! Books or resources that cover algebra and exponent rules could really help solidify your understanding. Look for titles that focus on problem-solving techniques in algebra or even online tutorials that provide step-by-step guidance.