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

To simplify the expression \( 35^{3} \cdot 35^{-9} \) to \( 35^{14} \), we can use the **Product Rule of Exponents**, which states that when multiplying two expressions with the same base, you add the exponents:

\[
a^m \cdot a^n = a^{m+n}
\]

In this case:

\[
35^{3} \cdot 35^{-9} = 35^{3 + (-9)} = 35^{-6}
\]

If you wanted to express \( 35^{-6} \) as a positive exponent, you'd apply the **Property of Negative Exponents**, which states that:

\[
a^{-m} = \frac{1}{a^{m}}
\]

Thus, \( 35^{-6} = \frac{1}{35^{6}} \).

So, the properties applied to generate the equivalent expression \( 35^{-6} \) from \( 35^{3} \cdot 35^{-9} \) are the **Property of Negative Exponents** and the **Product Rule of Exponents**.

Therefore, the correct response is:

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