A farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0), Q(1,1)$ and $R(2,0)$. From this land, a neighbouring farmer $\mathrm{F}_2$ takes away the region which lies between the side PQ and a curve of the form $y=x^n(n>1)$. If the area of the region taken away by the farmer $F_2$ is exactly $30 \%$ of the area of $\triangle \mathrm{PQR}$, then the value of n is $\_\_\_\_$ .