elementary number theory - If $gcd(a,b)=9,$ then what is $gcd(a^2,b^3),?$

I know that by the euclidean algorithm, I can obtain the following equations.

I tried some algebraic manipulation but I can't seem to determine, if

$$\text{if }\;\gcd(a,b)=9,\text{ then what is }\gcd(a^2,b^3)\;?$$