The power of an FM signal remains constant as the modulation index increases, as power only depends on the carrier amplitude and is independent of modulation index. The bandwidth of an FM signal increases as the modulation index increases, as more sidebands are generated. The bandwidth of AM and FM signals is the same when the modulation index is 1, as the number of sidebands is equal at this point. Increasing the modulation index widens the FM bandwidth but does not affect the total power.