What is the order when doing $x^{y^z}$ and why? Does $x^{y^z}$ equal $x^{(y^z)}$? If so, why? 
Why not simply apply the order of the operation from left to right? Meaning $x^{y^z}$ equals $(x^y)^z$?
I always get confused with this and I don't understand the underlying rule. Any help would be appreciated! 

I would just like to point out that many calculators share the OP's confusion, even calculators from the same manufacturer. Taking a quick sample from the lost-and-found box in my office, I found that 2^3^4 turned out to be: 


*

*4096 on Texas Instruments BA II Plus, TI-30XA, TI-30X II s, TI-36X solar, Windows calculator

*2.4178...*10^24 on Texas Instruments TI-30XS MultiView, Casio fx-115ES Plus, Google search bar.

