1. **State the problem:** Add the base six numbers 10542 and 3442. 2. **Convert base six numbers to base ten:** - For 10542 in base six: $$1 \times 6^4 + 0 \times 6^3 + 5 \times 6^2 + 4 \times 6^1 + 2 \times 6^0 = 1 \times 1296 + 0 + 5 \times 36 + 4 \times 6 + 2 = 1296 + 0 + 180 + 24 + 2 = 1502$$ - For 3442 in base six: $$3 \times 6^3 + 4 \times 6^2 + 4 \times 6^1 + 2 \times 6^0 = 3 \times 216 + 4 \times 36 + 4 \times 6 + 2 = 648 + 144 + 24 + 2 = 818$$ 3. **Add the base ten equivalents:** $$1502 + 818 = 2320$$ 4. **Convert the sum back to base six:** - Divide 2320 by 6 repeatedly and record remainders: - $2320 \div 6 = 386$ remainder $4$ - $386 \div 6 = 64$ remainder $2$ - $64 \div 6 = 10$ remainder $4$ - $10 \div 6 = 1$ remainder $4$ - $1 \div 6 = 0$ remainder $1$ - Reading remainders from last to first gives the base six number: $14424_6$ 5. **Final answer:** $$10542_6 + 3442_6 = 14424_6$$