Given that $a>1$a>1, fully simplify the expression $\log_a\left(a^9\right)$loga(a9).
Given that $a>1$a>1, fully simplify the expression $\log_a\left(\sqrt{a}\right)$loga(√a).
Given that $a>1$a>1, fully simplify the expression $\log_a\left(\frac{1}{a^2}\right)$loga(1a2).
Given that $a>1$a>1, fully simplify the expression $\log_a\left(\frac{1}{\sqrt{a}}\right)$loga(1√a).