It might help to understand a few laws of exponents:
Rule 1: (x^a)^(1/a)=x
Rule 2: x^a*x^b=x^(a+b)
Rule 3: x^a/x^b=x^(a-b)
Remember: If you can square both sides of something, you can take both sides to any power.
So in the first case you have something raised to the 2/3 power. Eliminate the exponent (Rule 1) by raising both sides to the 3/2 power. In the second case you have something raised to the 3/2 power so raise both sides to the 2/3 power. You get the idea.
The third case is requires more clever manipulation. First divide by both sides by (x-1)^1/2 getting 3x+2(x-1)^(3/2-1/2) (Rule 3)=3x+2(x-1)^1=3x+2(x-1)=0. Now we've gotten the exponent to disappear by dividing. Math is pretty cool that way sometimes.
Hope that helps.
