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.