is the quantity of 3x raise to zero raise to 1 half is equal to square root of 3?

Your problem can be interpreted 2 ways:

1. ((3x)^0)^(1/2) = 1^(1/2) = 1.

2. (3x^0)^(1/2) =
(3*1)^(1/2) = 3(^1/2)= sqrt(3).