To rewrite the expression for \( 10032 \) as a product of identical factors, we first need to factor the number.
Let's find the prime factorization of \( 10032 \).
- Divide by 2: \[ 10032 \div 2 = 5016 \]
- Divide by 2 again: \[ 5016 \div 2 = 2508 \]
- Divide by 2 again: \[ 2508 \div 2 = 1254 \]
- Divide by 2 again: \[ 1254 \div 2 = 627 \]
- Divide by 3 (next prime): \[ 627 \div 3 = 209 \]
- Divide 209 by its prime factors (it is \( 11 \times 19 \)):
- \( 209 = 11 \times 19 \)
Now, compiling all the factors: \[ 10032 = 2^4 \times 3^1 \times 11^1 \times 19^1 \]
Identifying the number of identical factors:
- The \( 2^4 \) means you can express this as \( (2^2 \times 2^2) \) or \( (4 \times 4) \).
Now, let's rewrite \( 10032 \) in a simplified form: \[ 10032 = 16 \times 627 \]
To express \( 10032 \) as a product of identical factors, we can take the 16 (which is \( 2^4 \)). Thus, the product can be expressed as: \[ 10032 = 16 \times 3 \times 11 \times 19 \]
But the most straightforward representation for identical factors would be as: \[ 10032 = (4^2) \cdot (3 \cdot 11 \cdot 19) \]
Final answer discussing identical factors: We can simply state: \[ 10032 = (16) \cdot (627) \text{ thus can say } = (4 \cdot 4) \cdot (3 \cdot 11 \cdot 19) \]
Hence, the expression for \( 10032 \) as a product of identical factors can be \( (16) \) of \( 627 \).
In the format requested, the simplest form is: \[ \boxed{10032 = 16 \cdot 627} \]