Question
Which expression is equivalent to start fraction, 3, to the power minus 7 , divided by, 3, to the power minus 1 , end fraction, question mark
3
−1
3
−7
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 3, to the power 6 , end fraction
3
6
1
start fraction, 1, divided by, 3, to the power 7 , end fraction
3
7
1
3, to the power 73
7
3, to the power 83
8
3
−1
3
−7
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 3, to the power 6 , end fraction
3
6
1
start fraction, 1, divided by, 3, to the power 7 , end fraction
3
7
1
3, to the power 73
7
3, to the power 83
8
Answers
GPT-4o mini
To simplify the expression \(\frac{3^{-7}}{3^{-1}}\), we can use the property of exponents which states that \(\frac{a^m}{a^n} = a^{m-n}\).
So, we have:
\[
\frac{3^{-7}}{3^{-1}} = 3^{-7 - (-1)} = 3^{-7 + 1} = 3^{-6}
\]
The expression \(3^{-6}\) can also be written as:
\[
\frac{1}{3^6}
\]
Therefore, the equivalent expression is:
\(\frac{1}{3^6}\)
Among the provided options, the correct answer is:
**start fraction, 1, divided by, 3, to the power 6 , end fraction**.
So, we have:
\[
\frac{3^{-7}}{3^{-1}} = 3^{-7 - (-1)} = 3^{-7 + 1} = 3^{-6}
\]
The expression \(3^{-6}\) can also be written as:
\[
\frac{1}{3^6}
\]
Therefore, the equivalent expression is:
\(\frac{1}{3^6}\)
Among the provided options, the correct answer is:
**start fraction, 1, divided by, 3, to the power 6 , end fraction**.