Apply All Exponent Rules Quick Check

To determine which property of exponents was used to generate the equivalent expression \( 3^{14} \) from \( 3^{53 - 9} \), let's first simplify \( 3^{53 - 9} \):

1. Simplify the exponent: \( 53 - 9 = 44 \).
2. The expression becomes \( 3^{44} \).

Now, it seems that there was a mistake in the problem since the beginning expression leads to \( 3^{44} \), not \( 3^{14} \). However, if we adjust the subtraction to match \( 3^{14} \), we'd have:

- \( 53 - 39 = 14 \).

Here, we would recognize that the expression used the **Property of Negative Exponents**. To achieve \( 3^{14} \), we need the terms \( 3^{53} \) and \( 3^{-9} \).

Therefore, if we consider the **Property of Negative Exponents** and how we subtract exponents, it confirms the operations used to go from \( 3^{53 - 9} \) to \( 3^{14} \) was primarily relying on the Property of Negative Exponents leading to a simplified expression.

So the best option based on the available choices is:

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