There is a test charge q₀ , and  vector r is its position vector.

vector r =xi +yj +zk

As we know that a vector quantity have both magnitude and direction.

The unit vector shows the direction of a vector and the magnitude we get as-

r = √(x² +y² +z²)  = (x² +y² +z²)^1/2

Now, E = (kq/r²) r^  ......(1)

Here, r^ is the unit vector, and we can write it as-

r^ = vector r/ r .....(2)

Now if we put the value of r^ in equation (1), we get-

E = (kq/r³) vector r

and the value of r =(x² +y² +z²)^1/2

Hence, E= (kq/(x² +y² +z²)^3/2) vector r