NinjaSharkSet5Problem1
First notice $ (x-c^\frac{1}{p})^p = x^p-c $.
So $ F(c^\frac{1}{p}) $ is the splitting field of $ x^p-c $.
Now suppose that the polynomial is reducible in some field K.
First notice $ (x-c^\frac{1}{p})^p = x^p-c $.
So $ F(c^\frac{1}{p}) $ is the splitting field of $ x^p-c $.
Now suppose that the polynomial is reducible in some field K.