1. **State the problem:** Find the remainder when the expression $\left(6^3 + 4^2 \times 2^1\right)$ is divided by 8. 2. **Write the expression:** $$\frac{6^3 + 4^2 \times 2^1}{8}$$ 3. **Calculate powers:** - $6^3 = 6 \times 6 \times 6 = 216$ - $4^2 = 16$ - $2^1 = 2$ 4. **Calculate multiplication inside the parentheses:** $$4^2 \times 2^1 = 16 \times 2 = 32$$ 5. **Sum inside the parentheses:** $$216 + 32 = 248$$ 6. **Divide by 8 and find remainder:** Divide 248 by 8: $$248 \div 8 = 31 \text{ remainder } 0$$ Since 8 times 31 is exactly 248, the remainder is 0. **Final answer:** The remainder is **0**.