What is the result of $2^{3^4}$?

Question

Simple question: what does $2^{3^4}$ equal to? I am asking this because some calculators take this as $2^{(3^4)}$ and others as ${(2^3)}^4$.

Answer 1

There is no "correct" answer per se. Because $(2^3)^4 \neq 2^{(3^4)}$, you should really specify which one you mean to avoid confusion. However, we most often decide that exponentiation associates to the right -- that is, $2^{3^4}$ is taken to mean $2^{(3^4)}$ -- because $(2^3)^4$ can also less confusingly be written as $2^{3 \cdot 4} = 2^{12}$.

Answer 2

If you write $a^{b^c}$ then most people take that as $a^{(b^c)}.$ If you write a^b^c, then almost everyone will stop and ask you where your parens are. Even Maple refuses to do the calculation without parens.

Answer 3

The answer is $$2^{3^4}$$ $$=2^{81}$$ Which means the order is from top to bottom i.e. $2^{(3^4)}$