Hi all, I've gone through the 'read before' threads so I hope this is in the right section and that I've typed it out ok, I'm still working with pen and paper here

Basically I've just started to get back into mathematics and I'm doing a course externally. I've had a try at simplifying the problem below but all the rules are a very new to me and so I have no idea if I'm on the right track or not. Any feedback at all would be a huge help, Thanks.

Simplify:

(z + 1)^2 (3xy^2)^3 / (9y^2)^1/2 x^-3 (z + 1) ^-1

= (z + 1)^2 (9x^3y^6) / 3y x^-3 (z + 1)^-1

= (z + 1) ^2 9x^3y^6 1/3y^-1 x^3 (z + 1)

= (z + 1)^3 9x^9y^6 1/3y^-1

= (z + 1)^3 3x^9y^-6

I've typed it out as I've done the steps because I'd almost guarantee the final answer is wrong so like I said any feedback on what I've done right or wrong would be a huge help.