The electric power consumed by a device may be calculated by using either of the two expressions P = I²R or P = V²/R. The first expression indicates that it is directly proportional to R whereas the second expression indicates inverse proportionality. How can the seemingly different dependence of P on R in these expressions be explained. 

Both the expressions are correct. In the first case, I remain constant whereas the second expression is true when V remains constant

So, the expression P = I²R is used when resistances are connected in series because in series connection the current in each resistance is constant.

Similarly, when resistances are connected in parallel the voltage is constant and so power becomes inversely proportional to R.