Prove that 9ⁿ cannot end with 0.

Given: 9ⁿ

To prove: 9ⁿ cannot end with 0.

Explanation:

We know all the composite numbers which ends with 0 have 10 as a factor.

So, this implies here for composite number 9, 10 is factor of 9ⁿ.

We have for any natural number p:

9ⁿ = 10 × p

⇒ (3× 3) ⁿ = 2 × 5× p

⇒ 3ⁿ × 3ⁿ = 2 × 5× p

That is 5 is prime factor of 3ⁿ × 3ⁿ which is not possible.

Thus, our assumption is wrong.

Hence 9ⁿ cannot end with 0.