2 cubed is smaller than 3 squared as 3x3 is bigger than 2x2x2.
Which is bigger 2 to the power of x or x to the power of 2?
I figured with some working on my attached sheet that when x is larger than 5. Then 2 to the power of x is always larger than x to the power of 2 as the previous number timesed by 2 is equal to the next number when x is larger or equal to 0. This is explained further on my sheet.
Which is bigger a to the power of x or x to the power of a. I figured when a<x then a to the power of x will always be bigger than x to the power of a and if x<a then a to the power of x will always be smaller than X to the power of a.
This is assuming x and a are both positive integers .
If x = a then a to the power of x is equal to x to the power of s.
See my sheet uploaded for examples and more details.