Question
Which property of exponents was used to generate the equivalent expression ^314
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
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
Answers
GPT-4o mini
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.)
\[
\frac{a^m}{a^n} = a^{m - n}
\]
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.)