Does the limit exist

$\lim _{ N\dashrightarrow \infty }{ { \left[ \left( { \left( { 2009 }^{ 2010 } \right) }^{ N } \right) +\left( { \left( { 2010 }^{ 2009 } \right) }^{ N } \right) \right] }^{ 1/N } }$ Let the value of the limit above equal to $\left| { \alpha }^{ \beta } \right|$ where $\alpha ,\beta \quad \epsilon$ N (Natural No.) then value of $\left( \alpha -\beta \right)$ is