# Why does this theorem for minimal sufficient from the "All of Statistics" textbook by Wasserman have these exponents of $n$?

In the textbook All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman, the definition of minimal sufficient is given as follows:

9.35 Definition. A statistic $$T$$ is minimal sufficient if (i) it is sufficient; and (ii) it is a function of every other sufficient statistic.

It then gives the following theorem:

9.36 Theorem. $$T$$ is minimal sufficient if the following is true: $$T(x^n) = T(y^n) \ \text{if and only if} \ x^n \leftrightarrow y^n.$$

Why does this theorem have these exponents of $$n$$? Having these exponents of $$n$$ doesn't really make sense to me.

In that book, $$n$$ random variables $$X_1, \dots, X_n$$, constituting the "data set", are represented as $$X^n$$. Whereas realisations of those $$n$$ random variables $$x_1, x_2, \dots , x_n$$ are represented as $$x^n$$.