What does a notation $R^X$ generally mean for a semiring $R$ and a set $S$?

Question

While going through a lecture note by a speaker named-Sam Payne, entittled-Tropical Scheme Theory (Idempotent Semirings), i encounter a notation $R^X$, saying that if $R$ is an idempotent semiring and $S$ is set then $R^X$ is an idempotent semiring. I couldn't figure out what does the notation $R^X$ mean?

Answer 1

If $X$ is a set and $R$ an algebraic structure (or just another set), then $R^X$ denotes the set of maps $X\to R$, on which we can define algebraic operations pointwise from the algebraic operations on $R$. Often, the same axioms that hold for $R$ also hold for $R^X$. For semirings, this is the case.