Take logs of each side:
So today you got it right!
HINT: If you want to check an answer put in values for the variables.
Let b=256 and a=2. Use logs to base 2.
The original equation becomes: 2^(24/5)=256^(3/5)=(2^8)^(3/5)=2^(24/5). So both sides of the equation are equal. This gives you confidence that you found the right answer.