576 = 26 x 32
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No. Every composite number has one unique prime factorization. You can write it with or without exponents, but it's still the same prime factorization.
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.
When all the factors are prime numbers, that's a prime factorization.
Prime factorization!