To generate the equivalent expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we can follow these steps:
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Apply the Property of Negative Exponents: Recall that \( a^{-n} = \frac{1}{a^n} \). So, \( 3^{-9} \) can be rewritten as \( \frac{1}{3^9} \).
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Using the Quotient Rule of Exponents: In general, the quotient rule states that \( \frac{a^m}{a^n} = a^{m-n} \). Here, we have: \[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]
Thus, both the Property of Negative Exponents and the Product Rule of Exponents (or in this case, the Quotient Rule) are used.
Therefore, the correct answer is: the Property of Negative Exponents and the Product Rule of Exponents.
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