Powers
Is a × a × a = 3 a ? Is a 3
= a × 3?
Or, should we guess what  is?
In mathematics, each symbol, (e.g. a ×3, 3a , a 3
) has a uniquely defined meaning. a × 3 has been arbitrarily
chosen as shorthand for a + a + a . It cannot mean anything else!
a 3 has been, equally arbitrarily, chosen as
shorthand for a × a × a. It means precisely this.
3 × a is shorthand for 3a, but note that the omission of the
× sign is possible only between a number and a letter (and only
in that order). Omitting it from any other combination would lead
to something different from a product, e.g. 33 is not 3 × 3 ; aa
or a3 means a single variable consisting of two symbols each.
Always consider the (unique!) meaning of the maths you write.
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