We study the power law equation governing the relationship between resistivity and temperatureof a superconductor, as well as the pressure-induced it's resistance and color change, through the generalized relational expression. By assuming a relationship between resistivity, effective mass and temperature, we find a generalized formula without gravitational effect and a generalized expression for the power law coefficient A. Through careful selection of the exponent N of the speed of light in vacuum, we obtain specific power law equations and a particular expression for A. In regards to the relationship between temperature and pressure, it has that the resistance varies inversely with pressure to the power of a third, sixth or half within a specific range. Similarly, in relation to color and pressure, the frequency varies directly with pressure to the power of a quarter, half, linearity, negative half, or inverse proportion. This indicates that the color shifts from blue to purple to blush as the pressure rises within a certain range. It shows that the expansion of the application of generalized relational expression can be achieved by appropriate choicing the exponent of the constants.