Question

Is 2^3^5^4 the same as 2^3^4^5.If not why? Please explain.

Answer 1

Its is no the same.
Lets take the last 2 powers 4^5 in 2nd section and 5^4 in the 1st one.
4^5 = 4×4×4×4×4= 1024
5^4 = 5×5×5×5 = 625
which is not the same. So both the values are not the same.
However if the powers are in barckets then its a whole other case entirely. If the powers are in brackets then the values of both are same. As in the case of bracketed powers you are multiplying the powers first and then applyed to the base And since multiplication is commutative it is the same in any order.