To rewrite \(\log\left(\frac{1}{81}\right)\) with a negative exponent, we can express \(\frac{1}{81}\) as \(81^{-1}\). Thus, we have:
\[ \log\left(\frac{1}{81}\right) = \log(81^{-1}) \]
Next, we apply the Power Rule of Logarithms, which states that \(\log(a^b) = b \cdot \log(a)\). In this case, \(a\) is \(81\) and \(b\) is \(-1\):
\[ \log(81^{-1}) = -1 \cdot \log(81) \]
Therefore, we can simplify this expression as:
\[ \log\left(\frac{1}{81}\right) = -\log(81) \]
This is the simplified form that uses a negative exponent and the Power Rule of Logarithms.