Given that $a^2 - \frac{6a}{b} + \frac{9}{b^2} = 0$, find the value of $ab$. Answer ab = ...

1. Identify the perfect square expression

$a^2-\frac{6a}{b}+\frac{9}{b^2}=\left(a-\frac{3}{b}\right)^2$
So,
$\left(a-\frac{3}{b}\right)^2=0$

2. Solve for $ab$

$a-\frac{3}{b}=0$
$a=\frac{3}{b}$
Multiplying both sides by $b$,
$ab=3$