Solve the commutator relations

[Juli]

Homework Statement

Solve $[\hat{r}^{17}, \hat{p}]$ and $[\hat{r}, \hat{p}^{250}]$

Relevant Equations

$[\hat{p}, \hat{x}^{n}] = - i \hbar n x^{n-1}$

Hello, I need to solve the commutator relations above. I found the equation above for the last one, but I am not sure, if something similar applys to the first one. I am a little bit confused, because I know there has to be a trick and you don't solve it like other commutator.
Thanks for your help!

 

[Orodruin]

Are you familiar with the expansion of a commutator on the form $[AB,C]$? If not, take the time to write it out and see if you can express it in terms of commutators containing only two operators.

 

[kuruman]

You understand, of course, that the relevant equation is what you need to prove. You can do this using mathematical induction and the identity suggested by @Orodruin.