Prime Factorization of 108:
To find the prime factorization of 108, we need to express it as a product of its prime factors. We can start by dividing 108 by the smallest prime number, which is 2.

108 ÷ 2 = 54

We continue dividing by 2 until we can no longer divide evenly:

54 ÷ 2 = 27

Now, we move on to the next prime number, which is 3:

27 ÷ 3 = 9

9 ÷ 3 = 3

Since 3 is also a prime number, we stop here. Therefore, the prime factorization of 108 is 2 × 2 × 3 × 3, or in exponential form, 2^2 × 3^2.

Prime Factorization of 192:
To find the prime factorization of 192, we follow the same process. We start by dividing 192 by 2:

192 ÷ 2 = 96

We continue dividing by 2:

96 ÷ 2 = 48

48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

Finally, we divide by 3:

6 ÷ 3 = 2

Since 2 is a prime number, we stop here. Therefore, the prime factorization of 192 is 2 × 2 × 2 × 2 × 2 × 3, or in exponential form, 2^5 × 3.

Product of Prime Factors:
To find the product of the prime factors of 108 and 192, we multiply their exponential forms:

2^2 × 3^2 × 2^5 × 3

Using the properties of exponents, we can simplify this expression:

2^(2+5) × 3^(2+1)

2^7 × 3^3

So, the product of the prime factors of 108 and 192 is 2^7 × 3^3.