# Homework Help: Another Really Easy Group Calculations which i cant do

1. Oct 27, 2008

### SNOOTCHIEBOOCHEE

1. The problem statement, all variables and given/known data
prove that if aba-1=b2

then a3ba-3=b8

3. 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 couldnt figure it out.

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

2. Oct 27, 2008

### 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 $$ab=b^2a$$

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