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To solve the worksheet, we'll express each number as a product of its prime factors in index notation.

### 1. Prime factorization of 20:
- 20 can be divided by 2: \( 20 \div 2 = 10 \)
- 10 can be divided by 2: \( 10 \div 2 = 5 \)
- 5 is a prime number.

Thus, the prime factorization of 20 is:
\[
20 = 2^2 \times 5
\]

### 2. Prime factorization of 360:
- 360 can be divided by 2: \( 360 \div 2 = 180 \)
- 180 can be divided by 2: \( 180 \div 2 = 90 \)
- 90 can be divided by 2: \( 90 \div 2 = 45 \)
- 45 can be divided by 3: \( 45 \div 3 = 15 \)
- 15 can be divided by 3: \( 15 \div 3 = 5 \)
- 5 is a prime number.

Thus, the prime factorization of 360 is:
\[
360 = 2^3 \times 3^2 \times 5
\]

### 3. Prime factorization of 375:
- 375 can be divided by 5: \( 375 \div 5 = 75 \)
- 75 can be divided by 5: \( 75 \div 5 = 15 \)
- 15 can be divided by 5: \( 15 \div 5 = 3 \)
- 3 is a prime number.

Thus, the prime factorization of 375 is:
\[
375 = 5^3 \times 3
\]

### 4. Prime factorization of 192:
- 192 can be divided by 2: \( 192 \div 2 = 96 \)
- 96 can be divided by 2: \( 96 \div 2 = 48 \)
- 48 can be divided by 2: \( 48 \div 2 = 24 \)
- 24 can be divided by 2: \( 24 \div 2 = 12 \)
- 12 can be divided by 2: \( 12 \div 2 = 6 \)
- 6 can be divided by 2: \( 6 \div 2 = 3 \)
- 3 is a prime number.

Thus, the prime factorization of 192 is:
\[
192 = 2^6 \times 3
\]

Would you like further explanations for any of the steps? Here are some related questions you could explore:

1. What is the difference between prime factorization and other factorizations?
2. How can prime factorizations help in finding the highest common factor (HCF)?
3. What is the least common multiple (LCM) and how do prime factors relate to it?
4. Why is 1 not considered a prime number?
5. How can you quickly find prime factors using division?

**Tip:** When performing prime factorizations, always start by dividing by the smallest prime number (2), and continue dividing by the smallest primes until you reach a prime number.

Use index notation to express each of the following numbers as a product of prime factors: 20, 360, 375, and 192.

Learn how to express numbers 20, 360, 375, and 192 as products of prime factors using index notation. This problem covers key concepts in prime factorization, exponentiation, and arithmetic, suitable for students in Grades 6-8.

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