We know that in a prism, the dispersion occurs in such a way that the rays of different colors are at some angle to each other. But this isn't the case in a parallel slab, the light rays of different color are parallel to each other after emerging from the other side of the slab. The reason why we don't see the component colors may be due to the mixing of the different colors, thus giving the white light again, but is it right to think so? Please elaborate.
Yes, indirectly it is due to mixing of colors. When the white light encounters the first air-glass interface, it disperses into different colors. Indeed if you were to somehow observe the light inside the slab, you will see different colors. However, the angle of dispersion created at the first interface is lost when the light encounter the second interface, when the different colors partly recombine to give back white light.