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

1 answer

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.