Question

State that 9 n cannot end with digit 0 for any natural number

Answer 1

For a number to end with 0 it's factorisation must contain , prime factors 2 and 5
But the factorisation of 9n only contain 3x3n . So there is no valueof n where 9n ends with a 0

Answer 2

9n cannot end in the digit 0 because in the prime factorisation of 9 it will be (3×3)^n , there is no 2 or 5. The fundamental theorem of arithmetic guarantees that 2 or 5 cannot come in the factorisation of 9.
Therefore 9^n cannot end in the digit 0 for any natural no: n.