To apply the Power Rule of Logarithms, we use the property that states:
\[ \log_b(a^c) = c \cdot \log_b(a) \]
In evaluating \(\log_{10} \frac{4}{5}\), we can rewrite it using the quotient rule:
\[ \log_{10} \frac{4}{5} = \log_{10} 4 - \log_{10} 5 \]
However, the Power Rule specifically relates to coefficients of logarithms. To use the Power Rule in this context, we need a proper expression where we can factor a base raised to an exponent.
None of the options provided (\(-\frac{4}{5} \log_{10}, -\frac{5}{4} \log_{10}, \frac{5}{4} \log_{10}, \frac{4}{5} \log_{10}\)) inherently apply the Power Rule correctly to evaluate \(\log_{10} \frac{4}{5}\).
Thus, none of the options accurately represent the application of the Power Rule on \(\log_{10} \frac{4}{5}\). Instead, they appear to be manipulations of \(\log_{10}\) without a clear basis for how they are transformed from \(\log_{10} \frac{4}{5}\).
If the goal is simply to rewrite \(\log_{10} \frac{4}{5}\) in relation to log10, the answer does not strictly follow the Power Rule, as there is no exponent applied to the log terms presented.
If this is designed as a conceptual question about the Power Rule or logarithmic transformation, please clarify further to address it accordingly.
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