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To completely factorize \(10,000\) and express the answer using exponents, let’s follow a similar approach shown in the examples.

### Step-by-Step Solution

1. Start by breaking down \(10,000\) into its prime factors.
2. \(10,000 = 100 \times 100\)
3. \(100 = 10 \times 10\)
4. Each \(10\) can be factored into \(2 \times 5\), so:

\[
10,000 = (2 \times 5) \times (2 \times 5) \times (2 \times 5) \times (2 \times 5)
\]

5. Counting the factors of \(2\) and \(5\), we find four \(2\)s and four \(5\)s.

6. Therefore, the prime factorization is:

\[
10,000 = 2^4 \times 5^4
\]

### Answer
\[
10,000 = 2^4 \times 5^4
\]

Would you like further details on this process, or do you have any questions?

### Related Questions

1. How do you factorize numbers that are not powers of 10?
2. What is the prime factorization of \(1,000,000\)?
3. How can you verify a prime factorization is correct?
4. How do exponents simplify repeated multiplication in prime factorizations?
5. What are common factorization methods for larger numbers?

### Tip
When factorizing large numbers, break them down into smaller, manageable parts, and use a factor tree if needed.

Factor each number completely. Write your answer with exponents. 10,000 = ?

Learn how to completely factorize 10,000 using prime factorization and express the answer with exponents. This step-by-step solution demonstrates the process, utilizing concepts of prime factors and exponents, ideal for students in Grades 5-7.

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