\[\left( \frac{b}{3} \right)^{2}\ :\left( \frac{b}{9} \right)^{3} = \frac{b^{2}}{3^{2}}\ :\frac{b^{3}}{3^{6}} =\]
\[= \frac{b^{2} \cdot 3^{6}}{3^{2} \cdot b^{3}} = \frac{3^{4}}{b} = \frac{81}{b}\]