### Instruction: What is the base ten equivalent of $12345_{6}$?### Response: This problem asks me to convert a number from base six to base ten.
I can use the place value method to do this.
Base six means that each digit represents a power of six, starting from the rightmost digit as the zeroth power.
So, $12345_{6}$ means $1 \times 6^4 + 2 \times 6^3 + 3 \times 6^2 + 4 \times 6^1 + 5 \times 6^0$.
I can evaluate each term and then add them up.
$1 \times 6^4 = 1296$, $2 \times 6^3 = 432$, $3 \times 6^2 = 108$, $4 \times 6^1 = 24$, and $5 \times 6^0 = 5$.
Adding them up, I get $1296 + 432 + 108 + 24 + 5 = 1865$.
So, the base ten equivalent of $12345_{6}$ is 1865.