Hi! I'm new to the forum, I'm learning maths from some textbooks over the aussie summer holidays and have no teacher or tutor, so I'm in here bothering you guys

I have to simplify some expressions without using 0 or a negative exponent, and got to this one:

** (2a^-1/3b^-2)^-2**
When I worked through it I got

**4a^2/9b^4** as the answer, but the textbook says the answer is

**9a^2/4b^4**. My working went as follows.

** (2a^-1/3b^-2)^-2**
=

** (2b^2/3a)^-2** << since it's 3b^(-2) and **not** (3b)^(-2), there is no negative exponent over 2 and 3.
=

** (2b^2)^-2/(3a)^-2**
=

** 9b^2*(-2)/4a^-2**
=

** 9b^-4/4a^-2**
=

** 9a^2/4b^+4**
I've worked through it a few times and can't figure it out. Can someone tell me where I went wrong? I want to sort it out before I go further.

p.s. I'd use the [tex] codes but they're not showing negative exponents properly when I preview. sorry