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 $F _ { 2 }$ takes away the region which lies between the side $P Q$ 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 $\triangle P Q R$, then the value of $n$ is $\_\_\_\_$.