Final answer:
To express the prime factorization of 144 as a product of prime factors, we can divide 144 by 2, then divide the result by 2 again, and finally divide the remaining number by 3.
Step-by-step explanation:
To express the prime factorization of 144 as a product of prime factors, we need to break down 144 into its prime factors. We can start by dividing 144 by the smallest prime number, which is 2. We find that 2 goes into 144 6 times, with a remainder of 0. So we can write 144 as 2^6 times some other number. Next, we divide that number by 2 again and find that it goes into the number 3 times, with a remainder of 0. So we can write 144 as (2^6)^(3) times some other number. Finally, we can divide the remaining number (9) by 3 and find that it goes into 144 3 times, with a remainder of 0. So we can write 144 as (2^6)^(3) times 3^2.