Which property of exponents was used to generate the equivalent expression ^314

Question

from 3^5/3^−9
3
5
3
−
9
?(1 point)
Responses

only the Property of Negative Exponents
only the Property of Negative Exponents

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

Answer 1

To generate the expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we apply the Property of Exponents that states:

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

In this case, we take:

• \( m = 5 \)
• \( n = -9 \)

So, applying the property:

\[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]

Thus, the correct response would be:

only the Product Rule of Exponents.

(Note: the term "Product Rule" in the context of your choices typically refers to multiplying like bases, but in this case, we're really using subtraction due to division, highlighting a potential misunderstanding in how the terms are named in your options.)