In PlanetMath there is an identity of commutators which I think is wrong. This identity is the fourth identity in Theorem 5 of this page. I think that the correct identity is this one, computed by me:
PlanetMath identity: $[x^z,y]=\left[x,y^{z^{-1}}\right]$, where $x^z=z^{-1}xz$
Identity computed by me: $[x^z,y]=\left[x,y^{z^{-1}}\right]^z$
Am i correct?