+641 We can solve this problem using the divisibility rule for 9. This rule states that a number is divisible by 9 if the sum of its digits is divisible by 9.
Divisibility Rule for 9: A number (like 8*10^18 + 1^18) is divisible by 9 if the sum of its digits is divisible by 9.
Simplifying the Expression:
8*10^18 can be written as 800,000,000,000,000,000 (eight hundred quadrillion).
The sum of the digits in 800,000,000,000,000,000 is 8 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 = 16.
Remainder When Divided by 9:
We need to find the remainder when 8*10^18 + 1^18 (which has a digit sum of 16) is divided by 9.
Since 18 is a multiple of 2, 1^18 will always be 1. So, we can focus on the divisibility of 800,000,000,000,000,000 (with a digit sum of 16).
We can find the remainder by subtracting the nearest multiple of 9 that is less than 16: 16 - 9 (nearest multiple of 9 less than 16) = 7.
Therefore, the remainder when 8*10^18 + 1^18 is divided by 9 is 7.
