Question

show that 9n can not end with a digit 0 for any n and N

Answer 1

9^n=(3×3)^n

a number which ends with digit 0 is always having 2 and 5 as it's factors
but there are no 2 or 5 as factors on the given number
therefore , 9^n cannot end with a digit zero for any natural number n

Answer 2

Hi friend,

For the number 9ⁿ to end with digit zero for any natural number n,it should be divisible by 2 and 5.

This means that the prime factorisation of 9ⁿ should contain the prime factors 2 and 5.

9ⁿ = (3²)ⁿ

It is not possible to express 9ⁿ as the product of prime factors,2 and 5.

So,there is no natural number n for which 9ⁿ ends with digit zero.

Hope it helps