Nuclear power does not change mass to energy. The energy is in the mass. Nuclear power is created when the energy in the mass is released,due to the atoms of mass being fused together by heat and pressure, or when atoms are split by being slammed together at very high velocity. Actually, energy and mass are basically the same thing. That's the meaning of E=(MC)2
The principle of conservation of energy predates Einstein's theory of relativity. We now know that energy can be created from mass and vice versa. However this requires a fusion reaction, so in everyday life we can rely on the basic conservation idea.