To simplify the expression \( \frac{3^5}{3^{-9}} \) and show that it is equivalent to \( 3^{14} \), we can use the Property of Negative Exponents and the Product Rule of Exponents.
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Property of Negative Exponents: This property states that \( \frac{a^m}{a^n} = a^{m-n} \). In this case, it applies as follows: \[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]
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Product Rule of Exponents: While not directly used in the simplification of the fraction, it is relevant here because we are multiplying by \( 3^{9} \) when rewriting the division into addition: \[ 3^{5} \cdot 3^{9} = 3^{5 + 9} = 3^{14} \]
Therefore, the correct answer is: the Property of Negative Exponents and the Product Rule of Exponents.