(84)12​=(?)8​

Solution:

Step 1 — Convert (84) from base 12 to decimal:

• 8 × 12 + 4 = 96 + 4 = 100 (decimal)

Step 2 — Convert 100 (decimal) to base 8 by repeated division:

1. 100 ÷ 8 = 12 remainder 4

2. 12 ÷ 8 = 1 remainder 4

3. 1 ÷ 8 = 0 remainder 1

Step 3 — Read the remainders from last to first: 1, 4, 4, so the base-8 representation is 144.

Check: 1×8^2 + 4×8 + 4 = 64 + 32 + 4 = 100, which matches the decimal value from base 12. Therefore, (84) in base 12 = (144) in base 8.