The number $10,000^{10,000}$ is extremely large, so it's best to break it down and express it in terms of powers of 10 for simplicity.

We know that $10,000 = 10^4$. So we can rewrite the original expression as:

$10,000^{10,000} = (10^4)^{10,000}$

By applying the power rule $(a^m)^n = a^{mn}$, we get:

$(10^4)^{10,000} = 10^{4 \times 10,000} = 10^{40,000}$

So, $10,000^{10,000}$ is equal to $10^{40,000}$.

This means the number has 40,001 digits — 1 followed by 40,000 zeros.

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. How do powers of 10 grow with different bases?
2. What is the number of digits in $10^n$ for large values of $n$?
3. How do you calculate powers with large exponents in scientific notation?
4. How does $1000^{1000}$ compare to $10,000^{10,000}$?
5. What are some real-world examples where powers of 10 are used?

Tip: To quickly estimate the number of digits of large powers, use the logarithmic property that the number of digits of a number $N$ is approximately $\log_{10}(N) + 1$.