1. Stating the problem: Simplify the expression $a^{\log_a b}$.\n\n2. Recall the logarithm power rule: For any positive $a \neq 1$ and positive $b$, $a^{\log_a b} = b$. This is because the logarithm $\log_a b$ is the exponent to which $a$ must be raised to get $b$.\n\n3. Applying the rule: Since $a^{\log_a b}$ means raising $a$ to the power that equals $b$, the expression simplifies directly to $b$.\n\nFinal answer: $$a^{\log_a b} = b$$