4x^3/4 = x^1/2Find x

We presume you want to solve 4x^(3/4) = x^(1/2). ( But kindly nor that 4x^3/4 = x^1/2 gives the meaning of (4x^3)/4 = (x^1)/2 , in which case  x^3 = x/2 Or x= 0 or x = + sqrt (1/2) or x = -sqrt(1/2) shall be the solution for x.

To solve the above equation.

If we raise both sides to the 4th power , we get integral exponents. So,

[4x^(3/4)]^4 = [x^(1/2)] ^(4).

256x^3 = x^2. Or

256x^3-x^2 = 0. Or

x^2(256x -1) = 0 . Or

x^2 = 0, Or  256x-1 = 0.

x^2 = 0 gives x= 0

256x-1 = 0 gives x = 1/256.

Aliter:

Also 4x^(3/4) = x^(1/2). Divding both sides by x^(1/2).

4x^(1/4) = 1

x^(1/4)  = 1/4 . S x = (1/4)^4.

Also you can go by x^(1/4) = t and  solve for x = t^4.