What is the remainder when \(9^{100}\) is divided by 8?
Answer: A
We can write the base 9 as \(8+1\). The expression becomes finding the remainder of \((8+1)^{100} \div 8\). According to the remainder theorem, this is equivalent to finding the remainder of \(1^{100} \div 8\). Since \(1^{100} = 1\), the remainder is 1.