To find how to generate the equivalent expression \(3^{14}\) from \(3^5\) as the numerator and \(3^{-9}\) as the denominator, we can apply the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m - n} \]
In this case, we have:
- The numerator is \(3^5\) (which means \(m = 5\)).
- The denominator is \(3^{-9}\) (which means \(n = -9\)).
Applying the property:
\[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]
Thus, the property of exponents used here is the quotient of powers property, which allows us to subtract the exponents when dividing like bases.