Type 2^3^2 into Google, and it restates it as 2^(3^2), which is 512.
The Windows calculator, which enforces order of operations (at least, entering 2+3*4 results in 14, not 20) says 64.
calculators use two main types of arithmatic which will produce different results if ( ) are not used.
TI calculators (and most others) use standard algrbraic operations.
HP and a few others use reverse polish notation which does operations in a different order if ( ) are not used.
On an HP calculator the last line would not work.
You use
2 enter
3 ^
2^
and the result is 64.
In your last line you have two operators in a row, which procedure does not work.
In your first line your notation is difficult in that you do not know whether you are dealing with 2 and 3 or 23. You could develop a computer program which would take care of this particular problem but you would still hve a problem with longer first numbers.
> how do you convert infix to postfix in case of exponents?
> is 2^3^2 in postfix
> 23^2^
> or
> 232^^
It depends on whether you have defined your exponent operator as left-associative or right-associative. I don't think there's any authoritative answer on this. Without defining your exponent operator as left-associative or right associative, a^b^c results in an ambiguous expression.
The first is correct
(23^)2^ = 82^ = 64
But 232^^ = 2(3^2)^ = 2 9^ = 512