To simplify the expression \(\log_4 64 - \log_4 16\) using the Quotient Rule of Logarithms, we start by recalling the Quotient Rule itself. The Quotient Rule states that:
\[ \log_b \frac{M}{N} = \log_b M - \log_b N \]
Using this rule, we can combine the two logarithmic terms. Here, \(M\) is \(64\) and \(N\) is \(16\):
\[ \log_4 64 - \log_4 16 = \log_4 \frac{64}{16} \]
Now, we need to simplify \(\frac{64}{16}\):
\[ \frac{64}{16} = 4 \]
Thus, we can rewrite the expression as:
\[ \log_4 \frac{64}{16} = \log_4 4 \]
Now, we know that \(\log_b b = 1\), so:
\[ \log_4 4 = 1 \]
Therefore, the final simplified expression is:
\[ \log_4 64 - \log_4 16 = 1 \]
In conclusion, the simplification of \(\log_4 64 - \log_4 16\) results in \(1\).