Difficult Question on Permutations

[PhysicsHelp12]

If you have a permutation writtein disjoint cycle notation ( I attatched it )

what's the minimum positive integer k such that t^k =Identity

t is tau

 

[CompuChip]

Can you reason what will happen when $\tau$ is multiplied by itself? And if you calculate $\tau^3$?
What will happen in general when we keep multiplying tau by itself?

 

[adriank]

Remember that disjoint cycles commute. Thus, if $\tau = \tau_1 \tau_2 \dotsc \tau_m$ is a product of disjoint cycles, then $\tau^n = \tau_1^n \tau_2^n \dotsc \tau_m^n$.

 

[CompuChip]

Very well adrian, although I was sort of hoping PhysicsHelp12 would figure that out by himself.