The speed at which the ball leaves the strings is determined by how much of the energy in its collision with the strings is returned. With a stiffer frame, less of the energy in the ball-racquet collision gets absorbed in deforming the frame materials, so more of that energy goes into deforming the string bed and the ball itself. One might expect that when the frame springs back to its original shape, it will return much of the energy it had absorbed, but by the time the frame springs back, around 15-20 milliseconds after impact, the ball, which leaves the strings within 5 milliseconds, is already gone. The energy used to deform the frame is thus wasted, but not so the energy stored by stretching the string bed and compressing the ball. The strings and the ball both rebound quickly enough to return much of their energy, so at a given impact speed between ball and frame, a stiffer racquet, which keeps more energy in the strings and the ball, returns more energy in the form of outgoing ball speed. In other words, a stiffer frame is more powerful.
At a given impact speed between ball and frame, a racquet with a higher swingweight is also more powerful. Swingweight generally increases with overall racquet weight and more of that weight placed in the racquet head. We won't elaborate on why greater swingweight increases power at a given swing speed, because it should make immediate sense from everyday experience: A heavier hammer drives a nail farther per strike. If you're familiar with momentum and kinetic energy, this should make even more sense, because both are directly proportional to mass.
So, we've reached essentially the same conclusion for gaining power as we had for reducing unexpected racquet twists and turns: Look for a stiffer racquet with more weight, especially in its head.
But, aren't power and control usually cast so that if you gain one, you lose some of the other? If all we wanted were maximal power and minimal twisting and turning, racquet selection would be a lot simpler than it is. Part of the problem is that there's a lot more to control than just the lack of twisting and turning.

