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# 2 to the 2 to the 22 power

I recently took the pamel (pennsylvania math league test thing) and for one of the questions it said: rearrange the numbers 2 in anyway with mathmatical symbols to get the highest number possible. I though the answer was 2 to the 222 power The answer was 2 to the 2 to the 22 power Is this correct? I thought that you would multiply the powers to get 2 to the 44 power, now have the power to the power and get 2 to the 4194304 power.

## Comments

13 years ago

(2 to the (2

^{22}) !) would be higher than that.13 years ago

Why not 2

^{2}2^{2? That would be 2}2^{256, which is bigger.}Reply 13 years ago

Mangled--two raised to two raised to two raised to two=two raised to two raised to 256

Reply 13 years ago

. Maybe it's a problem with notation/explanation, but 2**2**2**2 = 256. (IIRC, that's old FORTRAN notation for powers.)

. How's this: ((2

^{2})^{2})^{2}?13 years ago

This is how they positioned it

Reply 13 years ago

. Maybe I've forgotten my notation, but I read that as: two squared to the 22nd = two

^{44}Reply 13 years ago

that's what I though, but the math league says 2 to the 2 to the 22 (my carrot thingy button isn't working) is the same as 2 to the 4194304 power because 2 to the 22 power is 4194304.

Reply 13 years ago

and by the math league I mean something that is state wide

Reply 13 years ago

. There must be some missing parenthesis. According to Calc98 (desktop calculator): 2 x

^{y}2 x^{y}22 = 17592186044416. As does 2 x^{y}44.. Are you sure it wasn't written as 2 to the (2

^{22})?Reply 13 years ago

it could of been, I mean our teacher was just reading the answers aloud in an aututorium to about 600 people, so it could of been. But yeah with the parenthesis it's going to be a huuuuugggggeeeee number, a lot of calculators can't even handle it.

Reply 13 years ago

. Yeppers. I get "Overflow" when I try 2 to the 2

^{22}or 2^{4194304})13 years ago

. 2

^{2}22 = 2^{44 < 2}222. I'm guessing you read the question wrong. Or maybeI'mnot understanding what you're saying. :)Reply 13 years ago

. Wow! my formula got mangled.

. 2 squared to the 22nd power = 2 to the 44th, which is less than 2 to the 222nd power.