Check whether 4"

4ⁿ = (2²)ⁿ = 2²ⁿ

The only prime in the factorization of 4ⁿ is 2.

There is no other prime in the factorization of 4ⁿ is 2²ⁿ (By uniqueness of the fundamental Theorem of Arithmetic).

5 does not in the prime factorization of 4ⁿ for any n.

Therefore, 4ⁿ does not end with the digit zero for any natural number n.