Permutation/10/Explicit example/Exercise

Compute, for the permutation ${}\sigma$ given by

${}P$	${}1$	${}2$	${}3$	${}4$	${}5$	${}6$	${}7$	${}8$	${}9$	${}10$
${}\sigma (P)$	${}7$	${}10$	${}3$	${}9$	${}5$	${}2$	${}4$	${}1$	${}8$	${}6$

the powers ${}\sigma ^{2}$ and ${}\sigma ^{3}$ , and determine the cycle representation of these three permutations.