What does permutation stand for as a power?

Question

I am just reading some books about abstract algebra and I don't understand what a permutation stands for as a power.

For example, $(1 2)^{(1 2 3 \ldots n)}=(1 3)$.

Answer 1

Indeed, @Oliver hit the answer. A fact you may find useful is:

If $x$ and $y$ are two permutations of a set $\Omega$, such that $x=(\xi_1,\xi_2,...,\xi_k)$ then $$y^{-1}xy=(\xi_1^y,\xi_2^y,...,\xi_k^y)=x^y$$