The electric field due to an electric dipole at a distance r from its centre in axial position is E . If the dipole rotated through an angle of 90° about it perpendicular axis, the electric field at the same point will be

let the lenght of the dipole be d. if we rotate the dipole through 90 degrees then it will be come the case of electric feild due to dipole at a point in the equitorial plane. if we consider the vertical componenets at that point in electric field due to dipole(dEsin theta) they will cancel out each other and become zero. so the net electric field will be along the horizontal componenet that is 2dE cos theta. cos theta will be H/B thats is ({d/2}^2 + {r}^2)^ ½ where d/2 is half length of the dipole and r is the distance from the centre of the axis of the dipole. dE= kq/ {d/2}^1/2 + {r}^2  so finally when you multiply the power of {d/2}^2 + {r}^2 will become 3/2 as 1 +1/2 will be 3/2  so your final answer should be dE= kq/ [{d/2}^2 +{r}^2]^3/2.  hope you understood. please correct me if  am wrong. thank you.