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Let's perform the prime factorization of 252 and express it in index (exponent) form.

### Step-by-Step Prime Factorization:
1. Start by dividing 252 by the smallest prime number, 2:
   \[
   252 \div 2 = 126
   \]
2. Divide 126 by 2 again:
   \[
   126 \div 2 = 63
   \]
   Since 63 is odd, 2 is no longer a factor.

3. Next, divide 63 by 3 (the next smallest prime):
   \[
   63 \div 3 = 21
   \]
4. Divide 21 by 3 again:
   \[
   21 \div 3 = 7
   \]
5. Now, 7 is a prime number, so we stop here.

### Prime Decomposition in Index Form:
252 can be expressed as:
\[
252 = 2^2 \times 3^2 \times 7^1
\]

This is the prime factorization of 252 in index form.

Would you like more details or have any questions? Here are some related questions:

1. How can you verify that the prime decomposition of a number is correct?
2. What are the divisibility rules for 2, 3, and 7?
3. How do you find the prime factorization of a larger number?
4. Why is prime factorization useful in finding the greatest common divisor (GCD)?
5. Can every number be expressed as a unique product of primes?

**Tip**: Always start with the smallest prime number and proceed step by step to find the prime factorization of any composite number.

Write the prime decomposition of 252 in index form.

Learn how to find the prime decomposition of 252 and express it in index form. This problem covers key number theory concepts, including prime factorization and the fundamental theorem of arithmetic. Suitable for students in Grades 5-7.

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