Yes.
Prime factorization: 189 = 33*7.
This means:
a) The above equation is true.
b) Only prime numbers are used (except in exponents).
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No number has that prime factorization since 4 isn't prime.
No prime power exists since there are no duplicate prime numbers in the prime factorization.
The prime factorization is: 22 x 7
The prime factorization of the number 9600 would be 2 to the 7th power times 3 times 5 to the 2nd power.
113 is already prime. No factorization.