Question

prove that 8^n cannot end with 0​

Answer 1

Step-by-step explanation:

Given :-

8^n

To find :-

Prove that 8^n can not end with zero .

Solution :-

Given number = 8^n

It can be written as (2×2×2)^n

=> 8^n = (2×2×2)^n

=> 8^n = 2^n × 2^n ×2^n

We know that

If any number ends with zero then it must have 2 and 5 as factors in its prime factorization.

8^n have 2 in its prime factorization.

It has not 5 as one of the factors in its prime factorization.

So ,8^n does not end with zero.

Hence, Proved.

Answer:-

8^n does not end with zero for any natural number n .

Verification :-

Put n = 1 then 8¹ = 8

Put n = 2 then 8² = 8×8 = 64

Unit place is 4

Put n= 3 then 8³ = 8×8×8 = 512

Unit place is 2

If we do like this for any value for n

We do not get the unit place of 8^n is zero