Examine whether (4)ⁿ can end with the digit 0 for any n ϵ N.

If (4)ⁿ end with the digit 0, then the number should be divisible by 5.

As 2 × 5 = 10

This means the prime factorization of 4ⁿ should contain prime factor 5.

This is not possible because (4)ⁿ = (2²ⁿ), so the only prime in the factorization of 4ⁿ is 2. So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorization of 4ⁿ.

, 5 is not present in the prime factorization, there is no natural number nor which 4ⁿ ends with digit zero.

So, 4ⁿ cannot end with digit zero.