write each number as a product of prime factors. use exponentss where possible                                                   a. 49               b. 40               c. 72           d. 100               e   108           f.450

Here are the prime factorizations for each number:

**a. \( 49 \):**  
\[
49 = 7^2
\]

**b. \( 40 \):**  
\[
40 = 2^3 \times 5
\]

**c. \( 72 \):**  
\[
72 = 2^3 \times 3^2
\]

**d. \( 100 \):**  
\[
100 = 2^2 \times 5^2
\]

**e. \( 108 \):**  
\[
108 = 2^2 \times 3^3
\]

**f. \( 450 \):**  
\[
450 = 2 \times 3^2 \times 5^2
\]

Would you like further explanations on any of these factorizations?

Here are 5 related questions to expand your understanding:
1. What is the prime factorization of 144?
2. How can prime factorization help in finding the greatest common divisor (GCD)?
3. How does the prime factorization of a number relate to its square root?
4. What is the prime factorization of 600?
5. How can you use prime factorization to simplify fractions?

**Tip:** Always remember that prime numbers have only two divisors: 1 and the number itself!

Write each number as a product of prime factors. Use exponents where possible. a. 49 b. 40 c. 72 d. 100 e. 108 f. 450

Discover the prime factorization of numbers like 49, 40, 72, 100, 108, and 450. Learn how to break these numbers into their prime factors and express them using exponents. This lesson is ideal for students in Grades 6-8 studying number theory and exponents.

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