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2 to the 2 to the 22 power Answered

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.

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VIRON (author)2007-11-05

(2 to the (222) !) would be higher than that.

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CameronSS (author)2007-11-04

Why not 2222? That would be 22256, which is bigger.

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CameronSS (author)CameronSS2007-11-04

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

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NachoMahma (author)CameronSS2007-11-04

. 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: ((22)2)2 ?

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guyfrom7up (author)2007-11-04

This is how they positioned it

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NachoMahma (author)guyfrom7up2007-11-04

. Maybe I've forgotten my notation, but I read that as: two squared to the 22nd = two44

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guyfrom7up (author)NachoMahma2007-11-04

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.

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guyfrom7up (author)guyfrom7up2007-11-04

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

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NachoMahma (author)guyfrom7up2007-11-04

. There must be some missing parenthesis. According to Calc98 (desktop calculator): 2 xy 2 xy 22 = 17592186044416. As does 2 xy 44.
. Are you sure it wasn't written as 2 to the (222)?

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guyfrom7up (author)NachoMahma2007-11-04

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.

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NachoMahma (author)guyfrom7up2007-11-04

. Yeppers. I get "Overflow" when I try 2 to the 222 or 24194304)

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NachoMahma (author)2007-11-04

. 2222 = 244 < 2222. I'm guessing you read the question wrong. Or maybe I'm not understanding what you're saying. :)

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NachoMahma (author)NachoMahma2007-11-04

. Wow! my formula got mangled.
. 2 squared to the 22nd power = 2 to the 44th, which is less than 2 to the 222nd power.

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