SOLUTION: For what value of x is {{{ sqrt(x) ^sqrt(x) ^sqrt(x) =2^512}}}?

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Question 1097460: For what value of x is +sqrt%28x%29+%5Esqrt%28x%29+%5Esqrt%28x%29+=2%5E512?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Since the simplified expression is supposed to be a power of 2, it is highly likely that x itself is a power of 2.

Trial and error shows
4%5E4%5E4+=+4%5E256+=+2%5E512
and so
sqrt%28x%29+=+4
x+=+16