Which property of exponents was used to generate the equivalent expression 314 from 353−9 ?(1 point)

Question

Responses

only the Power Rule of Exponents
only the Power 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 Property of Negative Exponents
only the Property of Negative Exponents

only the Product Rule of Exponents

Answer 1

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

1. Property of Negative Exponents: This property states that \( a^{-n} = \frac{1}{a^n} \). In the expression \( 353 - 9 \), we interpret \( 53 \) as \( 5^3 \) and \( 9 \) as \( 3^2 \) to simplify.

2. Product Rule of Exponents: This rule states that \( a^m \cdot a^n = a^{m+n} \). In our example, the subtraction is handled in a way that it leads to multiplication of powers.

Therefore, the answer would be:

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