Examine whether (21)ⁿ can end with the digit 0 for any n ϵ N.

If (21)ⁿ end with the digit 0, then the number should be divisible by 2 and 5.

As 2 × 5 = 10

This means the prime factorization of 21ⁿ should contain prime factors 2 and 5.

But (21)ⁿ = (3 × 7)ⁿ and it does not have the prime factor 2 and 5 but have 3 and 7.

, 2 and 5 is not present in the prime factorization, there is no natural number nor which 21ⁿ ends with digit zero.

So, 21ⁿ cannot end with digit zero.