Apply All Exponent Rules Quick Check

Question

2 of 52 of 5 Items
Question
Which property of exponents was used to generate the equivalent expression 314 from 353−9?(1 point)
Responses

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
only the Product Rule of Exponents

only the Power Rule of Exponents

Answer 1

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.