Question

8^10-8^9-8^8 КРАТНО 11 Помогите пж

Answer 1

8^10 - 8^9 - 8^8 = 8^8 * ( 8^2 - 8 - 1 ) = 8^8 * ( 64 - 9 ) = 8^8 * 55 = 
= 8^8 * 5 * 11

Answer 2

To solve the problem, we need to determine whether the expression 8^10 - 8^9 - 8^8 is divisible by 11. We can do this using modular arithmetic.

First, we can simplify the expression by factoring out 8^8:

8^10 - 8^9 - 8^8 = 8^8 (8^2 - 8 - 1)

Now, let's consider the expression 8^2 - 8 - 1 modulo 11:

8^2 ≡ 64 ≡ 4 (mod 11) 8 ≡ -3 (mod 11) 1 ≡ 1 (mod 11)

So, we have:

8^2 - 8 - 1 ≡ 4 - (-3) - 1 ≡ 8 (mod 11)

Therefore, the original expression can be written as:

8^10 - 8^9 - 8^8 ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (8^2 - 8 - 1) ≡ 8^8 (