Which property of exponents was used to generate the equivalent expression 314 from 353−9 ?(1 point) Responses only the Property of Negative Exponents only the Property of Negative 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 Product Rule of Exponents only the Product Rule of Exponents only the Power Rule of Exponents

Answer 1

To generate the equivalent expression \( 314 \) from \( 353 - 9 \), the following properties of exponents were used:

1. Property of Negative Exponents: This property states that \( a^{-n} = \frac{1}{a^n} \). In this case, if we interpret \( 353 - 9 \) as \( 3^{53} \cdot 3^{-9} \) (since \( 3^{-9} = \frac{1}{3^9} \)), it results in division.

2. Product Rule of Exponents: This rule states that \( a^m \cdot a^n = a^{m+n} \). Therefore, \( 3^{53} \cdot 3^{-9} = 3^{53 - 9} = 3^{44} \).

To find \( 314 \), we can represent it as \( 3^{44} \) based on the manipulation shown.

So, the correct response is: the Property of Negative Exponents and the Product Rule of Exponents.