[tex]\displaystyle \left ( \frac{1}{2} - \frac{1}{6} :\frac{1}{3} \right)^{2009}= \\ \\ = \left ( \frac{1}{2} - \frac{1}{6} \times \frac{3}{1} \right)^{2009}= \\ \\ = \left ( \frac{1}{2} - \frac{1 \times 3}{6 \times 1} \right)^{2009}=\left ( \frac{1}{2} - \frac{1 }{2} \right)^{2009}= 0^{2009}=\boxed{0}[/tex]
