To generate the expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we use the following rules of exponents:
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Property of Negative Exponents: This states that \( a^{-n} = \frac{1}{a^n} \). Therefore, \( 3^{-9} \) can be rewritten as \( \frac{1}{3^9} \).
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Quotient Rule of Exponents: This states that \( \frac{a^m}{a^n} = a^{m-n} \).
Applying these properties, we have: \[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]
Thus, the equivalent expression was generated using the Property of Negative Exponents and the Quotient Rule of Exponents.
However, since "Quotient Rule of Exponents" was not one of the provided options, and assuming the "Product Rule of Exponents" is a typographical error or a mislabeling of the "Quotient Rule," the closest matching answer would be:
the Property of Negative Exponents and the Product Rule of Exponents.
(Please note the actual applicable exponent property here is the Quotient Rule, but from the given options, this would be the most correct response based on the context.)