[https://imgur.com/a/aiKWfXC](https://imgur.com/a/aiKWfXC)
I saw this meme posted on Facebook and I don’t understand. According to the comments, I am supposed to interpet this as 2\^18 = 262144, but why the square root? Also I thought that when it was a “power tower” of exponents like that, you worked from right to left, in which case it would be a ridiciously big number and certainly not be 262144?
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Anything after the 1 can be ignored as 1 to any power is 1.And you can ignore the 1 because anything to the power 1 is itself
So it’s the square root of 2^6^2. or 2^36
square root of 2^36 is 2 ^18 so yes – 262144
Unless I’m missing something since it’s early this equation is wrong. When stacking exponents like that you multiply the exponents. So 2^(6*2*1*4*4) =2^192. A square root is also x^(1/2). Multiply the exponents again you get 2^(192/2) =2^(96) = 7.9e28. So a very large number like you said.
Edit: someone pointed out that it should be interpreted as each exponent raised to the next instead of the entire base term in which case the equation does check out. 2^(6^2) instead of (2^6)^2
You can mostly evaluate this pretty easily up until the end.
You’re right that you evaluate right to left (top to bottom) as such:
sqrt(2^6^2^1^**4^4** ) = sqrt(2^6^2^**1^256** ) = sqrt(2^6^**2^1** ) = sqrt(2^**6^2** ) = sqrt(**2^36** ), where I’ve bolded the part of the exponent I’m evaluating at each step for clarity.
Then you can either evaluate sqrt(2^36 ) = 262144 as is, or further simplify (recall sqrt(2) = 2^1/2 ) as: 2^36/2 = 2^18 = 262144
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