I am trying to show that if $y$ is a cycle of length $r$, and $\sigma \in S_n$ then $\sigma y \sigma^{-1}$ is also a cycle of length $r$. More specifically, that if $y = (k_1\ \dots k_r)$ then $\sigma y \sigma^{-1} = (\sigma(k_1) \dots \sigma(k_r))$
I am not too sure how to show this. I know that $\sigma$ can be written as the product of disjoint cycles or length at least 2 by the cycle decomposition theorem, but am not sure how that helps.