Why is it incorrect to write 123 base 3 for eighteen?

Writing 123 base 3 for eighteen is incorrect because the representation of numbers in a specific base must only use digits valid for that base. In base 3, only the digits 0, 1, and 2 are allowed, while the digit 3 is invalid. The correct base 3 representation for eighteen is 200, as it translates to (2 \times 3^2 + 0 \times 3^1 + 0 \times 3^0 = 18).