(3x-1)^2/3=3/4
how do I find x?

Starting with:


(3x-1)^{2/3}=\frac 3 4


You can raise both sides to a factor of 1 over the (2/3) power, which is 3/2:


[(3x-1)^{2/3}]^{3/2}=(\frac 3 4)^{(3/2)}


Why do we do this trick? Recall that when raising a number w^a to the b power you get (w^a)^b = w^{ab}. If b is the inverse of a then you have (w^a)^{1/a} = w^1 = w. So raising both sides to the power of 1/a gets rid of the exponent on the left hand side. Applying this technique to your equation, where a = 2/3, turns the left hand side into:


[(3x-1)^{2/3}]^{3/2}=(3x-1)^{\frac 2 3 \times \frac 3 2 } = (3x-1)^1 = 3x-1


Can you take it from here?