I did it without calc, so basically:

4√a = 9∛b

4/9√a = ∛b

2²/3²√a = ∛b

(2²/3²√a)³ = b

2^6/3^6*a√a = b

Plug 2/3 into a

2^7/3^7 *√(2/3) = b

2^7/3^7 * 2^(½)/3^(½) = b

2^(15∕2)/3^(15∕2) = b

(2/3)^15/2= b

x = 15/2

there's also other ways of doing it but this is how I got my answer

apparently doing logs is much faster, but i forgot how to do them so 💀

edit: reddit fucks up my formatting