Sorting exponential numbers

Question

I want to sort some exponential numbers like {2^2,3^3,4^2} and i want The result {2^2,4^2,3^3}. But Mathematica Sort function apply's the powers in the result and return's {4,16,27}. How can i get the result in the same form as input?

Answer 1

All credits goes to J. M.'s technical difficulties♦

The trick is to use the Inactivate function to prevent Mathematica to apply the powers.

Inactivate[{2^2, 3^3, 4^2}, Power]

Then use SortBy function to compare the Active forms of the elements.

SortBy[Inactivate[{2^2, 3^3, 4^2}, Power], Activate]

Result:

{2^2,4^2,3^3}