Powers of cycles? Orders of elements?

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When calculating powers of cycles, are there any easy steps to use in doing so? I mean...is there a typical relationship when calculating (123)^n?

Also, is it safe to say that a ceratin n-cycle should have order n or n-1?

I guess any explanation of orders for group elements would be appreciated. For now I will look some stuff up on mathworld, etc. Thanks for your help.
 
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isn't it sort of obvious that any cycle of length n has order n?hence raising (123) to the nth power is the same as raising it to the least residue of n mod 3?
 

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