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d. \( \left(\frac{3^{7}}{3^{5}}\right)^{-2} \)

Ask by Ryan Donnelly. in Colombia
Mar 15,2025

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La respuesta es \( \frac{1}{81} \).

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Let's break it down! First, you can simplify the expression inside the parentheses: \( \frac{3^{7}}{3^{5}} \) equals \( 3^{7-5} = 3^{2} \). Now, you have \( (3^{2})^{-2} \). Using the power of a power property, you multiply the exponents: \( 3^{2 \cdot -2} = 3^{-4} \). This can be rewritten as \( \frac{1}{3^{4}} \), which is \( \frac{1}{81} \). So, the final answer is \( \frac{1}{81} \). It's like unwrapping layers of a gift - you simplify step-by-step to reach the exciting conclusion!

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