# What is the order when doing xyzx^{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!

In the usual computer science jargon, exponentiation in mathematics is right-associative, which means that $x^{y^z}$ should be read as $x^{(y^z)}$, not $(x^y)^z$.
In expositions of the BODMAS rules that are careful enough to address this question, the rule is to evaluate the top exponent first. One way to help remember this convention is to note that $(x^y)^z = x^{yz}$ (i.e., $x^{(yz)}$), so it would be silly if out of the two possibilities, $x^{y^z}$ meant the one that can be expressed without using two tiers of superscripts.