Powers
Is a Ã— a Ã— a = 3 a ? Is a ^{3}
= a Ã— 3?
Or, should we guess what is?
In mathematics, each symbol, (e.g. a Ã—3, 3a , a^{ 3}
) has a uniquely defined meaning. a Ã— 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 Ã— a Ã— a. It means precisely this.
3 Ã— a is shorthand for 3a, but note that the omission of the
Ã— 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 Ã— 3 ; aa
or a3 means a single variable consisting of two symbols each.
Always consider the (unique!) meaning of the maths you write.
