A question from a math noob...

Is there a way to simplify the following? $$2^{2^{n-1}}$$

Thanks in advance!

  • $\begingroup$ In general, exponents in a "tower" like that are hard to simplify. Maybe you could try $$2^{2^{n - 1}} = 2^{2^{n}/2} = \sqrt{2}^{2^{n}}$$ $\endgroup$ – Joshua Wang Feb 1 at 3:23
  • $\begingroup$ Welcome to MSE! Please use the basic tutorial and quick reference guide and also show the work you have done so far. $\endgroup$ – Laufen Feb 1 at 3:24
  • 2
    $\begingroup$ Sometimes simpler is in the eye of the beholder, but here I don't see any improvement available. $\endgroup$ – Ross Millikan Feb 1 at 3:27

Not really. $2^{2^{n-1}}$.

If it’s part of an equation you can take the log $2^{n-1} log 2$. Another log and you get $(n-1)log 2 + log log 2$.


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