3. \( c^{-5} d^{7} \)
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The Deep Dive
Did you know that negative exponents actually indicate a reciprocal? For your expression \( c^{-5} d^{7} \), you can rewrite \( c^{-5} \) as \( \frac{1}{c^{5}} \), transforming it to \( \frac{d^{7}}{c^{5}} \). This makes calculations clearer and more straightforward, especially in algebra! In real-world applications, manipulating expressions with exponents is crucial, particularly in fields like physics or engineering. For instance, when dealing with formulas for exponential growth or decay, simplifying complex expressions gives clarity. It's like decluttering your workspace—when it's tidy, you can focus on designing those impressive structures or analyzing exciting data without the extra chaos!