In which of the following expressions has prime factorization been done?

To determine which of the provided expressions represents a correct prime factorization, we need to break each number down into its prime factors:

• a) 24: 24 can be factored as 2 x 12, and 12 can be further factored into 2 x 6, and 6 can be factored into 2 x 3. Thus, the prime factorization of 24 is 2 x 2 x 2 x 3, or 2³ x 3.
• b) 56: 56 can be factored as 7 x 8, where 8 can be further factored into 2 x 4, and 4 can be factored into 2 x 2, resulting in the prime factorization of 56 as 7 x 2³.
• c) 70: This can be factored directly into 2 x 35, and 35 can be factored into 5 x 7. Therefore, the prime factorization of 70 is 2 x 5 x 7.
• d) 54: 54 can be factored as 2 x 27, and 27 can be further factored into 3 x 9, and 9 can be factored into 3 x 3. Hence, the prime factorization of 54 is 2 x 3³.

Now we check which expressions correctly represent prime factorizations:

• a) 24 = 2 x 3 x 4 is incorrect as it does not only consist of prime factors.
• b) 56 = 7 x 2 x 2 x 2 is correct.
• c) 70 = 2 x 5 x 7 is correct.
• d) 54 = 2 x 3 x 9 is incorrect as 9 is not a prime number.

Based on this analysis, the correct answers where prime factorization has been done are b) 56 and c) 70.