Question

show that 9n cannot end with 2 for any natural number​

Answer 1

If 9^n end with 2 it must have 2 in its prime factorization(That is it must be a multiple of 2). 9^n = 3^n * 3^n

We can see prime factorization on 9^n does not contain 2. Hence it can't end with 2.

Answer 2

Answer:

Step-by-step explanation:

If 9^n can end with the digit 2, then it must have the factors of 2.

But the prime factorisation of 9 is (3×3).

So, by the uniqueness of fundamental theorem of arithmetic 9^n cannot end with the digit 2.