To generate the expression \(3^{14}\) from \( \frac{3^5}{3^{-9}} \), the relevant properties of exponents used are:
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The Property of Negative Exponents: This states that \(a^{-n} = \frac{1}{a^n}\). Therefore, \(3^{-9} = \frac{1}{3^9}\).
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The Quotient Rule of Exponents: This states that \(\frac{a^m}{a^n} = a^{m-n}\). When applying this, we have:
\[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14}. \]
Thus, both the Property of Negative Exponents and the Quotient Rule of Exponents were used in the derivation.
The correct choice would be the Property of Negative Exponents and the Product Rule of Exponents, if the "Product Rule" was intended to refer to combining the exponents after applying the quotient rule.
If strictly looking at the operation carried out in the steps described, you could also say it's primarily the use of the Quotient Rule and the handling of the negative exponent that directly resulted in \(3^{14}\).
However, if you have to choose one from your options, the most specific reference should focus on the Property of Negative Exponents and the Quotient Rule of Exponents to arrive at that conclusion. So it seems like the references provided might not fully align with standard terminology. If you need to pick from the defined options, the option The Property of Negative Exponents and the Product Rule of Exponents can be justified as the choice that includes the negative exponent property used in this operation.