Question 36542
(2sqrt3x)^4

(2)^4 * (sqrt3x)^4
16 * sqrt3x * sqrt3x * sqrt3x * sqrt3x

As sqrt3x * sqrt3x = 3x
16 * 3x * 3x 
144(x^2)


As you had requested me to explain the last 2 lines, i will give an example

a^2 = a * a
sqrt(a^2)= sqrt(a)*sqrt(a)
sqrt(a^2)= sqrt(a*a)
sqrt(a^2)= a

The square and the sqaure root cancel each other resulting in  "a"

Similarily 
sqrt3x * sqrt3x * sqrt3x * sqrt3x
sqrt(3x * 3x)* sqrt(3x * 3x)
3x *3x

I hope it is clear now.