Show that $\alpha^k\tau\alpha^{-k}=(k+1, k+2)$

Question

Given $\alpha = (1, 2, 3, ... , n)$ and $\tau = (1, 2)$

Show that $\alpha^k\tau\alpha^{-k}=(k+1, k+2)$

I'm having trouble figuring out what $\alpha^k$ is. I know that I can split $\alpha$ up into transpositions but I think overall I'm just stuck and need a hint. Is there any exponentiation rule that I may be missing?