If 7n has to end with the digit 0 for any natural number n,
then it has to be divisible by 10.
ie. its prime factorisation should have the factors of both 2 and 5 [ since 10=2x5 ]
But we know that 7=7x1
By the fundamental theorem of arithmetics, we also know that there exist no other factors for 7.
Thus we conclude that 7n cannot end with the digit 0 for any natural number n.