Y^X - read as "y to the xth power" may not seem intuitive but it truly is - on both HP and TI calculators. For discussion, we can refer to the 'y' value by its real name, 'base', and the 'x' value by its real name, 'exponent'.
In fact, the name has to be 'weird' to have the arguments entered in 'natural' order.
Real HP calcs have a 4-level stack (X,Y,Z, and T registers), and also a LastX register too. So to perform this calc we key in
   [B]base[/B] [ENTER] [B]exponent[/B] [Y^X]
After ENTER is hit, the base value is lifted to the Y register, and the X register receives the exponent.
On TI/AOS calcs, Y^X works similarly but with infix, not postfix notation:
   [B]base[/B] [Y^X] [B]exponent[/B] [=]
On these calcs, the 'held value' - the base - gets stored in a "y" register pending calculation. (That's why you'll also see an [x<>y] (exchange x with y) on many of these calcs.
Bill Wiese
San Jose