To rewrite \( \log\left(\frac{1}{100}\right) \) using the Power Rule of Logarithms, we first recognize that \( \frac{1}{100} \) can be expressed as \( 100^{-1} \).
Applying the Power Rule, which states that \( \log\left(x^k\right) = k \cdot \log(x) \), we have:
\[ \log\left(\frac{1}{100}\right) = \log\left(100^{-1}\right) = -1 \cdot \log(100) \]
Now we can further simplify \( \log(100) \). Since \( 100 = 10^2 \), we can apply the Power Rule again:
\[ \log(100) = \log(10^2) = 2 \cdot \log(10) \]
Now substituting this back into our earlier expression gives:
\[ \log\left(\frac{1}{100}\right) = -1 \cdot (2 \cdot \log(10)) = -2 \cdot \log(10) \]
The result is:
\[ \log\left(\frac{1}{100}\right) = -2 \log(10) \]
Thus, the correct response is:
−2 log 10.