Express the prime factorization of 1,200 as a product of prime numbers with exponents.(2 points)
_4 ⋅_ ⋅_ 2 = 1,200
To express the prime factorization of 1,200 as a product of prime numbers with exponents, we can start by dividing it by the smallest prime number, which is 2.
1,200 divided by 2 is 600. So we can write it as:
1,200 = 2 * 600
Now, we need to continue factoring 600. We can still divide it by 2:
600 divided by 2 is 300. So we can write it as:
1,200 = 2 * 2 * 300
Next, we continue factoring 300:
300 divided by 2 is 150. So we can write it as:
1,200 = 2 * 2 * 2 * 150
Now, we need to find the next prime factor of 150. One way to go about this is to try dividing it by the next prime number, which is 3:
150 divided by 3 is 50. So we can write it as:
1,200 = 2 * 2 * 2 * 3 * 50
Finally, we need to factor 50. By dividing it by 2, we get:
50 divided by 2 is 25. So we can write it as:
1,200 = 2 * 2 * 2 * 3 * 2 * 25
Now, since 25 is a perfect square, we can further factorize it into 5 * 5:
1,200 = 2 * 2 * 2 * 3 * 2 * 5 * 5
Expressing it as a product of prime numbers with exponents, we can simplify it as:
1,200 = 2^4 * 3^1 * 5^2