Question

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

only the Property of Negative Exponents

Answer 1

To generate the expression \( 314 \) from \( 353 - 9 \), we need to analyze the given expressions.

Starting with \( 353 - 9 \):
1. We have \( 353 \), which can be rewritten as \( 35^{3} \).
2. The expression \( 353 - 9 \) suggests we're subtracting \( 9 \) from \( 53 \), which is not directly related to the manipulation of exponents.
3. To match the target of \( 314 \), we can rewrite \( 35^{3} \) in a way that uses negative exponents.

Using the property of negative exponents:
\[
a^{-n} = \frac{1}{a^{n}}
\]

We could also look at the Product Rule of Exponents:
\[
a^{m} \cdot a^{n} = a^{m+n}
\]

However, neither of these directly aligns with the given transformation without additional context.

Upon closer examination, it appears that \( 353 - 9 \) simplifies to \( 35^{3} \times 10^{-9} \), which is where both the Property of Negative Exponents (for the subtraction of the exponent) and the Product Rule (if we consider different exponent bases) come into play.

In conclusion, the best choice that reflects the transformations involved here is:
**the Property of Negative Exponents and the Product Rule of Exponents.**