i think you need more conditions on h. after all, 1 is a positive integer, and if u is in K (for any element u of L), then we get m = n.
Let p be a prime, and let m and n be positive integers such that m divides n. Let h be a positive integer as well. Let L be a field of order p^n, and let u be an element of L. L has a unique subfield K of order p^m.
Prove that u^h is in K.
Any help please?