To apply the Power Rule of Logarithms to evaluate \( \log_{10}(45) \), we can express 45 in terms of its prime factors:
\[ 45 = 9 \times 5 = 3^2 \times 5 \]
Using properties of logarithms, we can break this down:
\[ \log_{10}(45) = \log_{10}(3^2 \times 5) = \log_{10}(3^2) + \log_{10}(5) = 2\log_{10}(3) + \log_{10}(5) \]
The power rule states that \( \log_b(a^n) = n \log_b(a) \). Here, in the term \( \log_{10}(3^2) \), we applied the power rule by bringing down the exponent of 2.
Now, regarding the provided answer choices, none seem to match the direct calculation derived from \( \log_{10}(45) \).
If these answer choices intend to suggest that you'd apply the properties of logarithms further (for example, using approximations), you might need to check if those choices presented variations of some manipulation involving \( \log_{10}(3) \) or \( \log_{10}(5) \), acknowledging that the results may lead to approximations or calculative uses.
However, strictly speaking to just the Power Rule as applied directly to \( \log_{10}(45) \) (which can be reframed but retains its logarithmic nature), the answer directly falls within a different computation.
Therefore, unfortunately, I can't ascertain any transformed logarithmic versions provided in the choices that validly translate the power rule to achieve \( \log_{10}(45) \) directly.
Feel free to share more contexts or information perhaps related to numerical evaluations or approximations if those were intended!