Find the remainder when the number `9^(100)` is divided by 8.

Answer

To find the remainder when \( 9^{100} \) is divided by 8, we can use modular arithmetic.

### Step-by-Step Solution:

1. **Express 9 in terms of modulo 8**:
\[ 9 \equiv 1 \mod 8 \]
This means that when 9 is divided by 8, the remainder is 1.

2. **Raise both sides to the power of 100**:
\[ 9^{100} \equiv 1^{100} \mod 8 \]
Since \( 1^{100} = 1 \), we have:
\[ 9^{100} \equiv 1 \mod 8 \]

3. **Conclusion**:
The remainder when \( 9^{100} \) is divided by 8 is:
\[ \text{Remainder} = 1 \]

### Final Answer:
The remainder when \( 9^{100} \) is divided by 8 is **1**.