The number 10,000 (10k) is an even number because it can be divided by 2 without leaving a remainder. Mathematically:

$10,000 \div 2 = 5,000$

Since the result is a whole number, 10k is even. This holds true for any expression where 10,000 is involved as an independent term. However, if you're referring to expressions involving operations with 10k, whether the final result is odd or even depends on the operations used.

For example:

1. Addition with an odd number:
   $10,000 + 3 = 10,003$ (odd)
2. Multiplication by an odd number:
   $10,000 \times 3 = 30,000$ (even)
3. Subtraction of an even number:
   $10,000 - 4 = 9,996$ (even)
4. Division by an odd number:
   $10,000 \div 5 = 2,000$ (even)
5. Addition of an even number:
   $10,000 + 6 = 10,006$ (even)

Would you like details on any specific operations?

Related Questions:

1. What is the difference between an odd and an even number?
2. How can you determine if a product of two numbers is even or odd?
3. How do addition and subtraction affect the parity (odd/even) of a number?
4. What is the parity rule for division of two integers?
5. What happens to the parity when exponentiation is involved?

Tip: If you add two even numbers, the result will always be even.