5. Check whether 6ⁿ can end with the digit 0 for any natural number n.

A number ends with digit 0 if it is divisible by 10.

10 = 2 × 5

6ⁿ = (2 × 3)ⁿ

Thus, 6ⁿ contains only the prime factors 2 and 3 and does not contain factor 5.

Therefore, 6ⁿ cannot be divisible by 10.

Hence, 6ⁿ cannot end with the digit 0 for any natural number n.