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Without other symbols raising to a power is the only possible function.
Convention is that abc is interpreted as a(bc).
With only one raising to a power there are 3 places that the operation can fit: 2222,2222,2222. These are, respectively, 6.739986666787576 x 1066, 3.414278773642187 x 1029 and 49284.
There are also three ways of placing two power operators among the four 2's: 2222, 2222 and
2222. They equate to 2.06506 x 101262611, 4.994797680505552 x 10145 and 234256, respectively. (The largest of these need to be done using logarithms, as the numbers themselves will exceed the capacity of a calculator.)
Finally, 2222 = 65536.
The largest is 2222 = 2.06506 x 101262611. This was calculated as 222 = 4194304. Multiply this by log102, to get 1262611.314933419. The integer part of this is the power of 10 and the antilog of the fractional part (the mantissa) is the 2.06506.
There is a less standard notation, for something called "tetration", mentioned within MathWorld's page on Power Tower, which is the same thing under a different name and notation. This yields even larger numbers than mere exponentiation. See Dej Mar's solution. |
