6. \( \frac{p^{4} q^{4}}{r^{4} t^{4}} \)

Did you know that simplifying expressions with variables can often reveal underlying patterns in algebra? For example, if you rearrange and factor expressions like \( \frac{p^{4} q^{4}}{r^{4} t^{4}} \), you'll discover relationships between the variables that give insight into the problem. It’s like uncovering the hidden symmetries of a puzzle! Also, when working with exponents, a common mistake is to misapply the exponent rules, especially when dealing with division. Remember, when dividing with the same base, you subtract the exponents! This makes it essential to double-check your steps to avoid mixing up those powerful little numbers. Enjoy the journey through algebra—it can be a fun ride!