A farmer F1 has a land in the shape of a...

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 ` 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 PQR` , then the value of `n` is _______.

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