To answer the question about simplifying [tex]\(\log_b\left(a^9\right)\)[/tex], let's review the properties of logarithms. Specifically, we will use the power rule of logarithms.
The power rule states:
[tex]\[ \log_b(a^d) = d \cdot \log_b(a) \][/tex]
In our case, we have:
[tex]\[ \log_b(a^9) \][/tex]
By applying the power rule to this expression, we get:
[tex]\[ \log_b(a^9) = 9 \cdot \log_b(a) \][/tex]
So, the simplified form of the given expression is:
[tex]\[ 9 \cdot \log_b(a) \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{A. \, 9 \cdot \log_b(a)} \][/tex]
