prove by induction that for elements x and g of a group,

(x^-1.g.x)^n=x^-1.g^n.x

My working.

I've done the easy parts, showing true for n=1, assuming true for n=k but now given that, I need to show true for n=k+1.

I worked with LHS, expanding the braket and trying to manpiulate to get an expression I already knew but I'm pretty stumped.

Thanks for any help.