Another Really Easy Group Calculations which i cant do

[SNOOTCHIEBOOCHEE]

Homework Statement

prove that if aba^-1=b²

then a³ba^-3=b⁸

The Attempt at a Solution

Ive tried lots of different things, none of which have worked.

i trield left and right multiplying by a^2 and a^-2 but couldn't figure it out.

I know there is some magical trick but i cannot for the life of me figure it out.

 

[jhicks]

There's no real way to give you a hint so I'll just do the first step:

Note that $$ba^{-1}=a^{-1}b^2$$ and $$ab=b^2a$$

$$a^3ba^{-3}=a^2b^2a^{-2}=aabba^{-1}a^{-1}$$