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The prime factorization of a perfect cube (other than 0 or 1) will only have exponents that are...

A) odd numbers
B) even numbers
C) multiples of 3
D) multiples of 2

1 Answer

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Final answer:

Option (C), The prime factorization of a perfect cube (other than 0 or 1) will only have exponents that are multiples of 3.

Step-by-step explanation:

The prime factorization of a perfect cube (other than 0 or 1) will only have exponents that are multiples of 3.

To understand why, let's take an example. Suppose we have a perfect cube like 27. The prime factorization of 27 is 3 3. Here, the exponent 3 is a multiple of 3, and it represents the number of times the prime factor 3 is multiplied by itself.

Similarly, if we have a perfect cube like 64, the prime factorization of 64 is 2 6. Here, the exponent 6 is also a multiple of 3, representing that the prime factor 2 is multiplied by itself six times.

Therefore, the correct answer is C) multiples of 3.

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