Which one is preferred: $r2^m$ or $2^m r$?

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Which is preferable to write: $r2^m$ or $2^m r$?

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Usually $2^m r$ is more preferable.

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I think $r2^m$ is usually used, because if we write r at the end it is sometimes confused with $2^{mr}$

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Normally you would write literal constants first followed by variables in alphabetical order.

e.g. $256pq^2r$

So, using this scheme, the preferred syntax would be: $2^mr$

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I would say that there is no general preference, some will prefer the first while the other prefer the second.

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I don't think it matters too much if it is typed but if it is handwritten then I prefer $r2^m$ for the reasons pointed out by Shobhit. When typing also, I would prefer $r2^m$ if the exponent became too big. Typing $r2^{a + bc + d + efg}$ is clearer and more aesthetically pleasing than $2^{a + bc + d + efg}r$.

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The general rule is: in a product, write the numerals before the letters; and write the constants before the variables. Here, the exponent $m$ complicates the issue, and we would usually write $x\mathrm e^x$ in preference to $\mathrm e^xx$. (However, $\mathrm e^xy$ is arguably as natural as $y\mathrm e^x$.) In the present example, we are probably thinking of $2^mr$ as a generic form for $r$, $2r$, $4r$, and so on; so the $2^m$ tends to inherit the first position.