1) Let x(t) be the power signal which has finite nonzero power, such that

The later part of the equation is energy of signal.

If Energy is finite here, then power would become zero, which is contradictory to the statement we made in the beginnng.

Hence for Power to be finite and nonzero, Energy must be infinite.

2) Let x(t) be the energy signal with Energy E=constant (finite). The power of this signal can be expressed as,

But here later part of the limit represents signal energy. Hence

As Energy is finite, and limit tends to infinity into 1/(2T) will result in zero. Hence Power=0

Hence Power of an Energy signal is zero.