Fractional Exponents

I'm a bit confused. Why is it that:

(a^1/3) ^2 = a^2/3

But:

(x^1/2) (x^2) = x^5/2

Does it mean that x^2 = x^4/2?

Then why isn't it a^7/3 (a^1/3+6/3) for the first one?

And for this problem, why is 2/3 x 2/3 = 4/9 and not 4/3?

I think what really confuses me is when to multiply fractional exponents like fractions and when to only multiply the numerator.

Thank you very much for your help.

Edit: Added a second problem.