Mistake:
Step 2
Instead of multiplying it should divide:
(5a^2/ 9b^2) / (3a / b^2 a)
(5a^2 / 9b^2) * (b^2a / 3a)
5a^2b^2 / 27b^2a
b^2 / b^2 = 1
a^2 / a = a
5a / 27
