To generate the equivalent expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we can first apply the Property of Exponents related to division, which states that when we divide two expressions with the same base, we subtract the exponents:
\[ \frac{3^a}{3^b} = 3^{a-b} \]
In this case, \( a = 5 \) and \( b = -9 \):
\[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]
We also utilized the Property of Negative Exponents, since dividing by \( 3^{-9} \) is equivalent to multiplying by \( 3^9 \), which is another way to think about handling the negative exponent.
Therefore, the correct option that encompasses both the subtraction of exponents and the handling of the negative exponent is:
the Property of Negative Exponents and the Product Rule of Exponents.
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