What does $F^{\times 2}$ mean, for $F$ Field

Question

I would love some explanation regarding this notation, seen in "Quaternion Algebras" by John Voight, https://math.dartmouth.edu/~jvoight/quat-book.pdf in Prop. 2.2.10 and 2.2.14

Let $F$ be a field of $char \neq 2$ and $F^\times$ it's set of invertable elements, what is $F^{\times 2}$ ?

Answer 1

This refers to the set of square elements of $F^\times$, that is the set of $x\in F^\times$ such that $x=y^2$ for some $y\in F^\times$.

Answer 2

Sorry, yes, in general if $G$ is an abelian group written multiplicatively and $n$ is a positive integer, I write $G^n := \{g^n : g \in G\} \leq G$ for the subgroup of $n$th powers. Here, $G=F^\times$ and we drop the parentheses $F^{\times 2} = (F^\times)^2$.