Simplify expression without using zero or negative indices

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**

=

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

=

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

=

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

=

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

=

** 4a^2/9b^-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