Kimberly wants to define $3^{3^3}$ as $(3^3)^3$ but Nermeen thinks that such a stack of powers should be defined as $3^{(3^3)}$ .
Do their definitions lead to the same numerical value? Is the same true if $3$ is replaced with some other number?
How would Kimberly's and Nermeen's definitions most naturally extend to the definition of $3^{3^{3^3}}$? Do their definitions lead to the same numerical value? Is the same true if $3$ is replaced with some other number?