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!