Suppose I wanted to enact the calculation of elements of S6 in cycle notation of:
$((1234)(56))^{10}$ where the numbers in both brackets are raised to the power $10.$
My teacher has the answer as $(13)(24)$ but he has not explained this, I assume that I would have from $((1234)(56))^{10}= (1234)^{10}(56)^{10}$ (since the brackets commute).
And then if I break the indice down to let $(1234)^{10} = ((1234)^2)^5$ I get $((13)(24))^5$. Do we ignore the $(56)$ here?
Please explain this, my exam is in two days. And my understanding is really lacking for questions such as these.