### Instruction: What is the product of the digits in the base 8 representation of $6543_{10}$?### Response: I need to convert 6543 from base 10 to base 8 first.
I can use repeated division by 8 and write down the remainders.
6543 divided by 8 is 817 with a remainder of 7.
817 divided by 8 is 102 with a remainder of 1.
102 divided,by 8 is 12 with a remainder of 6.
12 divided by 8 is 1 with a remainder of 4.
1 divided by 8 is 0 with a remainder of 1.
So the base 8 representation of 6543 is 14617.
Now I just need to multiply the digits: 1 x 4 x 6 x 1 x 7.
That gives me 168.