Let's first break down the prime factorization of 192.

We begin by dividing 192 by 2, since it is an even number:

• 192 ÷ 2 = 96
• 96 ÷ 2 = 48
• 48 ÷ 2 = 24
• 24 ÷ 2 = 12
• 12 ÷ 2 = 6
• 6 ÷ 2 = 3

Since 3 is not divisible by 2, we stop there. Now we are left with:

• 3 is a prime number.

So, the prime factorization of 192 is: $192 = 2^6 \times 3$

In this case:

• $a = 6$
• $b = 3$

Thus, the values of $a$ and $b$ are 6 and 3, respectively.

Would you like further details on prime factorization or have any other questions? Here are some related questions for you:

1. How do you perform the prime factorization of other numbers?
2. What are the applications of prime factorization in mathematics?
3. How can you express prime factorization in exponential form?
4. What is the significance of the prime factorization in finding the greatest common divisor (GCD)?
5. How do you find the least common multiple (LCM) using prime factorization?

Tip: When performing prime factorization, start with the smallest prime number (2) and keep dividing until you can no longer divide evenly.