The correct option is C x3n+12
Given that,
F∝xn⇒F=kxn .....(1)
Here, the force is a variable force as it depends on the position of the particle.
Hence, the acceleration can be written as a=vdvdx
we can rewrite (1) as,
mvdvdx=kxn
Seperating the variables and integrating on both sides, we get
m∫vdv=k∫xndx
⇒v22=kmxn+1(n+1)+C
⇒v∝xn+12
We know from the definition of power, P=Fv
i.e P∝⎡⎢⎣xn×xn+12⎤⎥⎦⇒P∝x3n+12
Thus, option (c) is the correct answer.