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I can help you with the prime-power factorization of each number on the sheet. Let’s go through each problem one by one:

1. **48**:  
   \( 48 = 2^4 \times 3^1 \)

2. **35**:  
   \( 35 = 5^1 \times 7^1 \)

3. **46**:  
   \( 46 = 2^1 \times 23^1 \)

4. **40**:  
   \( 40 = 2^3 \times 5^1 \)

5. **66**:  
   \( 66 = 2^1 \times 3^1 \times 11^1 \)

6. **100**:  
   \( 100 = 2^2 \times 5^2 \)

7. **75**:  
   \( 75 = 3^1 \times 5^2 \)

8. **72**:  
   \( 72 = 2^3 \times 3^2 \)

9. **65**:  
   \( 65 = 5^1 \times 13^1 \)

10. **81**:  
    \( 81 = 3^4 \)

11. **80**:  
    \( 80 = 2^4 \times 5^1 \)

12. **54**:  
    \( 54 = 2^1 \times 3^3 \)

13. **972**:  
    \( 972 = 2^2 \times 3^5 \)

14. **660**:  
    \( 660 = 2^2 \times 3^1 \times 5^1 \times 11^1 \)

Would you like more details on how any of these factorizations were found, or do you have any further questions?

Here are 5 relative questions:
1. How can prime-power factorizations help simplify mathematical expressions?
2. What is the prime-power factorization of 144?
3. How do you find the greatest common divisor (GCD) using prime factorization?
4. What is the prime-power factorization of 90?
5. How can prime factorization be used to solve least common multiple (LCM) problems?

**Tip**: When breaking a number down into primes, always start by dividing by the smallest prime number (2), then work your way up!

Write the prime-power factorization of each.

Explore prime-power factorizations with examples like 48, 35, and more. Learn how each number breaks down into prime factors using the fundamental theorem of arithmetic. Suitable for middle school students in Grades 6-8.

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