What do stacked numbers next to a variable without parentheses represent?

Question

What do the $r_1$ and $r_2$ mean in the below expression?

$$Z_2 / Z_1 = \pi r_1^2 / t(r_2 - r_1)$$

Answer 1

$r_1$ and $r_2$ are indexed variables, It's sometimes used to denote members of a sequence. More often, it's simply a way to save variable names, or to link them in some other way. The stacked numbers are an exponent on top of an index. You could also have something like $$\raise{8px}{\Tiny5}(r_1)$$ which is tetration(repeated exponentiation) of $r_1$ . At least if $r_1$ is a variable. If $r$ was an operator like: $$\prod$$ or $$\sum$$ but typed inline, the 1 and 2 would represent lower and upper bounds on a variable respectively. If $r_1$ were a function, with an input such as: $$\sigma_1(x)$$ ,then the 1 may mean a specific form of the function, the 2 could then mean iteration (repeatedly applying the function, to it's own outputs). With sets they typical are used to represent rings or groups, or subsets. This whole formula reminds me of an inner circle to annulus surface area ratio personally.

EDIT if a line is present, that's a sign it's a fraction. etc. arguably it can stand for anything the author wants as long as it's defined as such.

Answer 2

If you refer to the $r_1^2$, it would arguably be more clearly written as $(r_1)^2$. In that light it becomes clear: the $1$ is a subscript, usually an index. The $2$ here is a superscript, which usually denotes a power (i.e. you are squaring the $r_1$ term).

Granted, these are not guarantees, and the convention can vary from context to context. But considering the lone $r_1$ term later in the expression, I feel $r_1^2$ just means "$r_1$ squared."

As for what specifically the $r_1,r_2$ refer to, I honestly wouldn't know from that screenshot alone.