Express each of the following as a product of prime factors only in exponential form:

`108xx192`

Answer

To express the product of 108 and 192 as a product of prime factors in exponential form, we will follow these steps:

### Step 1: Prime Factorization of 108
1. Start with 108.
2. Divide by 2:
\[ 108 \div 2 = 54 \quad \text{(so, } 108 = 2 \times 54\text{)} \]
3. Divide 54 by 2:
\[ 54 \div 2 = 27 \quad \text{(so, } 54 = 2 \times 27\text{)} \]
4. Divide 27 by 3:
\[ 27 \div 3 = 9 \quad \text{(so, } 27 = 3 \times 9\text{)} \]
5. Divide 9 by 3:
\[ 9 \div 3 = 3 \quad \text{(so, } 9 = 3 \times 3\text{)} \]
6. Finally, 3 is a prime number.

So, the prime factorization of 108 is:
\[ 108 = 2^2 \times 3^3 \]

### Step 2: Prime Factorization of 192
1. Start with 192.
2. Divide by 2:
\[ 192 \div 2 = 96 \quad \text{(so, } 192 = 2 \times 96\text{)} \]
3. Divide 96 by 2:
\[ 96 \div 2 = 48 \quad \text{(so, } 96 = 2 \times 48\text{)} \]
4. Divide 48 by 2:
\[ 48 \div 2 = 24 \quad \text{(so, } 48 = 2 \times 24\text{)} \]
5. Divide 24 by 2:
\[ 24 \div 2 = 12 \quad \text{(so, } 24 = 2 \times 12\text{)} \]
6. Divide 12 by 2:
\[ 12 \div 2 = 6 \quad \text{(so, } 12 = 2 \times 6\text{)} \]
7. Divide 6 by 2:
\[ 6 \div 2 = 3 \quad \text{(so, } 6 = 2 \times 3\text{)} \]
8. Finally, 3 is a prime number.

So, the prime factorization of 192 is:
\[ 192 = 2^6 \times 3^1 \]

### Step 3: Combine the Prime Factorizations
Now, we combine the prime factorizations of 108 and 192:
\[ 108 \times 192 = (2^2 \times 3^3) \times (2^6 \times 3^1) \]

### Step 4: Use the Property of Exponents
Using the property of exponents \(a^m \times a^n = a^{m+n}\):
1. Combine the powers of 2:
\[ 2^2 \times 2^6 = 2^{2+6} = 2^8 \]
2. Combine the powers of 3:
\[ 3^3 \times 3^1 = 3^{3+1} = 3^4 \]

### Final Result
Thus, the product of 108 and 192 expressed as a product of prime factors in exponential form is:
\[ 108 \times 192 = 2^8 \times 3^4 \]