Cessna 172 pilot reported multiple bounces on landing that resulted in a prop strike and nose gear damage.

Narrative

I departed ZZZ1 and flew north to the practice area where I practiced commercial maneuvers including chandelles; lazy 8s; a steep spiral and 8s on pylons. I then proceeded to ZZZ to practice power-off 180s. After 3 successful landings; I decided to finish the day with one more power-off 180. I executed a side-slip to lose altitude and came into ground effect over the runway at 71 knots; runway XX. The aircraft bounced on the runway upon landing. I attempted to go-around by bringing the flaps to 20 and adding full power. I bounced several more times; at least 50 feet in the air; maybe higher. Each time I was able to keep the wings level. I'm not sure if the initial porpoise turned into an elevator stall or not. By the last bounce; I was running out of runway and unable to stop the bouncing. The nose gear had been damaged and the propeller had hit the ground on the last bounce. My headset fell off and iPad dislodged from the yoke mount due to the intensity of the bounce. I secured the engine by pulling the mixture out and shutting off the magnetos; master and standby battery. I somehow landed on the runway without bouncing again and was able to taxi off of the active runway. I was uninjured and the ZZZ team towed the aircraft to the FBO.