# For a finite extension $F$, can we always find a an element a in $F$ s.t $\{a^t\}_{t= 0,…,n-1}$ is a basis of $F$?

Let $$K$$ be a field and $$F$$ be a finite extension of $$K$$ with degree $$n$$. Then can we always find a an element a in $$F$$ s.t $$\{a^t\}_{t= 0,...,n-1}$$ is a basis of $$F$$ ?

For example, if we had constructed $$L/K$$ as $$K(b) = L$$, then $$\{b^t\}_{t=0, ..,r-1}$$ where $$r$$ is the degree of the minimal polynomial of $$b$$, would form a basis for $$L$$;however, is this possible in general ?