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For questions pertaining to power towers: expressions like a^(b^(c^d))), which result from iterated exponentiation. The "hyperoperation" tag may be appropriate, too.

Power towers are obtained by iterated exponentiation; an archetypal example is:

$\large a^{b^{c^d}}$

Power towers have been studied a lot; there is particularly many information on:

  • Modular arithmetic with power towers;
  • Convergence of "infinite" power towers; for example: $$\large\sqrt2^{\sqrt2^{\sqrt2^{\cdots}}} = 2$$

If we have a (finite) power tower with the same number repeated, such as the one with $\sqrt 2$ above, we speak of tetration. Tetration is the fourth hyperoperation, so if applicable, also include the tag.

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