I have been looking over this cycle and permutation business in an abstract algebra book I have. One of the problems says to prove that the kth power of a permutation equals the identity.

$\displaystyle {\sigma}=(a_{1} \;\ a_{2} \;\ .... \;\ a_{k})\in S_{n}$.

Prove that $\displaystyle (a_{1} \;\ a_{2} \;\ ..... \;\ a_{k})^{k}=e$

How do we find the power of a permutation?. i.e $\displaystyle (1 \;\ 2 \;\ 3 \;\ 4 \;\ 5)^{3}$.

I can't seem to find it explained anywhere.