Question

Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^-9

only the Product Rule of Exponents
only the Product Rule of Exponents

the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents

only the Power Rule of Exponents
only the Power Rule of Exponents

only the Property of Negative Exponents

Answer 1

To generate the equivalent expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we can follow these steps:

1. **Apply the Property of Negative Exponents:** Recall that \( a^{-n} = \frac{1}{a^n} \). So, \( 3^{-9} \) can be rewritten as \( \frac{1}{3^9} \).

2. **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**.