How to find $2^{2^{2^{2^0}}}$?

Question

What is the result of $2^{2^{2^{2^0}}}$?

Answer 1

Power towers are grouped down from the top, so take the top $2^0=1$, then proceed downward.

Answer 2

$2^{2^{2^{2^0}}}=2^{2^{2^1}}=2^{2^2}=2^4=16$

Answer 3

Given problems like this, we always have to start from the topmost exponent and base which here is 0 and 2 respectively. So we have $ 2^0=1 $ and then proceeding likewise we have $ 2^1=2 $ and $ 2^2=4$ and finally, $ 2^4=16 $ as the answer.

Answer 4

From Order of operations

If exponentiation is indicated by stacked symbols, the usual rule is to work from the top down, because exponent is right-associative in mathematics.

thus:

$a^{b^c}$ = $a^{(b^c)}$

which typically is not equal to $(a^b)^c$

Basically, exponentiation implies brackets around the exponent.

Thus, this boils down to $2^{2^{2{^{2^0}}}}$. So then:

$2^0 = 1$, so that makes $2^{2^{2{^1}}}$

$2^1 = 2$, so now we’re at $2^{2^2}$

$2^2 = 4$, so we get $2^4$

$2^4 = 16$, and that's our answer.

Seems simple enough.