Express the prime factorization of 1,200 as a product of prime numbers with exponents.
To find the prime factorization of 1,200, we can start by dividing it by the smallest prime number, which is 2.
1,200 ÷ 2 = 600.
Now we divide 600 by 2 again:
600 ÷ 2 = 300.
We keep dividing by 2 until we can no longer divide evenly:
300 ÷ 2 = 150.
150 ÷ 2 = 75.
Now we try the next prime number, which is 3:
75 ÷ 3 = 25.
After that, we try dividing by 5:
25 ÷ 5 = 5.
Finally, we're left with the prime number 5, which cannot be divided further.
The prime factorization of 1,200 can therefore be expressed as:
2² × 3 × 5².
So, the prime factorization of 1,200 as a product of prime numbers with exponents is 2² × 3 × 5².