To simplify the expression \( 12523 \) by rewriting it as a product of identical factors, we first check if it can be factored into a perfect square or another form.
The number 12523 does not seem to be a perfect square, nor does it have simple factor pairs, so let's try to factor it.
To start, let's check the prime factorization of 12523:
- Check divisibility by small prime numbers (2, 3, 5, etc.).
- The number is odd, so not divisible by 2.
- The sum of digits \( 1 + 2 + 5 + 2 + 3 = 13 \), not divisible by 3.
- It doesn’t end in 0 or 5, so not divisible by 5.
- Continue checking divisibility with prime numbers.
Eventually, through testing factors or computational help, we find:
\( 12523 = 13 \times 11 \times 97 \).
Since there are no repeated prime factors, \( 12523 \) cannot be expressed as a product of identical factors. Therefore, \( 12523 \) is simplified as is.
Thus, the expression cannot be simplified further into identical factors.
Final answer: \( 12523 \) (as it is, cannot be factored into identical factors).