A farmer $F_1$ has a land in the shape of a triangle with vertices at $P\left(\mathrm{0,\; 0}\right),Q\left(\mathrm{1,\; 1}\right)$ and $R\left(\mathrm{2,\; 0}\right).$ From this land, a neighbouring farmer $F_2$ 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 $\mathrm{30\%}$ of the area of $∆PQR,$ then the value of $n$ is