$N = 5^{\displaystyle 5^{\displaystyle 5^{\displaystyle 5^{\displaystyle 5}}}}$
In the following equation is N equal to $5^{5^4}$ or $5^{(5^{(5^{(5^5)})})}$?
One of them is huge compared to the other, so knowing this would make a huge difference. Thanks.
On
Pretend that you're a computer trying to parse that expression. You see 5 raised to something, so you first need to parse and evaluate that something. But that something is 5 raised to something else, so you need to parse and evaluate that something else first. Keep going that way and you'll see that you need to parse and evaluate the top-most $5^5 = 3125$. Then you go back down one level, and so on. The result is huge!
As presented, your number would normally be interpreted as
$$ 5^{\displaystyle\left(5^{\left(5^{\left(5^{\left(5^{}\right)}\right)}\right)}\right)} $$ or, in tetration notation, ${}^55$.