Use a factor tree to break 192 into its prime factors. Then write 192 as the product of its prime factors in index notation.

Step 1: Start by finding any two factors of 192. For instance, we can start with 2 and 96 because 2*96 = 192.

Step 2: Continue to break down each composite number until all factors are prime. 96 can be broken down into 2 and 48, 48 can be broken down into 2 and 24, 24 can be broken down into 2 and 12, 12 can be broken down into 2 and 6, and finally, 6 can be broken down into 2 and 3.

So, the factor tree looks like this:

192 | 2 - 96 | 2 - 48 | 2 - 24 | 2 - 12 | 2 - 6 | 2 - 3

Step 3: Write 192 as the product of its prime factors. From the factor tree, we can see that the prime factors of 192 are 2 and 3. Counting the number of times each factor appears, we have six 2's and one 3.

So, 192 = 2 * 2 * 2 * 2 * 2 * 2 * 3

Step 4: Write the prime factorization in index notation. In index notation, we write the base (the prime number) and use an exponent to indicate the number of times the base is used as a factor.

So, 192 = 2^6 * 3^1