Dear student
$P={I}^{2}R$ and $P=\frac{{V}^{2}}{R}$ are basically the same relation. First one is usually used when I is constant and second one when V is constant.
Using $I=\frac{V}{R}$ one can be derived from the other.
$P={I}^{2}R={\left(\frac{V}{R}\right)}^{2}R={V}^{2}R$
In the case of parallel circuits when V is constant we use V2/R.But in the case of the series circuit when I is constant we use I2R.
Resistance is the property of the material and the resistance of a conductor depends upon the nature of its material, such as length of the conductor, cross-sectional area of the conductor, temperature, etc. It does not depend on power. Electric power is basically a derived quantity, which we derive by using Ohm's law and it is not the basic property. Thus you can not conclude that power is directly or inversely proportional to the resistance. However, the electric power of an electric circuit depends on the current and voltage, since it is the function of current flows through it against a potential difference.
Regards

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