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

Question

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 Power Rule of Exponents
only the Power Rule of Exponents

only the Product Rule of Exponents

Answer 1

To understand how the expression \( 353 - 9 \) generates \( 314 \), we need to break down the original expression using exponent properties.

The expression \( 353 - 9 \) can be simplified as follows:

1. The exponent \( 353 \) is equivalent to \( 3^{53} \).
2. The term \( -9 \) can be interpreted using the Property of Negative Exponents: \( a^{-n} = \frac{1}{a^n} \).

So, \( 353 - 9 \) can be rewritten as:

\[ 3^{53} \cdot 3^{-9} = 3^{53 - 9} = 3^{44}. \]

This shows that we used the Property of Negative Exponents along with the Product Rule of Exponents, which states that \( a^m \cdot a^n = a^{m+n} \).

Thus, the correct response is:

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