Question

Show that any number of the form 8^n, n€N, can never end with zero

Answer 1

Let x be the final outcome of 8ⁿ.

So, x = 8ⁿ

⇒ x = (2³)ⁿ

⇒  x = 2³ⁿ

This implifies that x has only one factor and that is 2.

Thus, x has no factor called 5 or in more precise way x is not divisible by 5.

Since a number must be divisible by 5 to end with 0. Hence 8ⁿ cant end with 0.

Q.E.D

Answer 2

Answer:

8ⁿ cannot end with zero.

Step-by-step explanation:

We know 8ⁿ = (2³)ⁿ = 2³ⁿ

If 8ⁿ end with zero then 10 is factor of 8ⁿ.

8ⁿ = 2³ⁿ = (5) (2)

It implies that 5 is factor of 2, which is a contradiction.

here 8^n = (2*4)^n doesn't have 5 in its prime factorization.

So, our assumption is wrong.

Hence 8ⁿ cannot end with zero.