1. **Problem statement:** Convert the number $7 \times 8^3 + 8 + 6$ to base 8. 2. **Recall:** Base 8 (octal) numbers use digits 0 to 7. To express a number in base 8, we convert the decimal number to base 8. 3. **Calculate the decimal value:** $$7 \times 8^3 + 8 + 6 = 7 \times 512 + 8 + 6 = 3584 + 8 + 6 = 3598$$ 4. **Convert 3598 to base 8:** Divide 3598 by 8 repeatedly and record remainders: - $3598 \div 8 = 449$ remainder $6$ - $449 \div 8 = 56$ remainder $1$ - $56 \div 8 = 7$ remainder $0$ - $7 \div 8 = 0$ remainder $7$ Reading remainders from last to first: $7 0 1 6_8$ 5. **Final answer:** $$7 \times 8^3 + 8 + 6 = 7016_8$$