Express the prime factorization of 1200 as a product of prime number with exponets

To express the prime factorization of 1200, we first factor it down into its prime numbers.

1. Start by dividing by the smallest prime number, which is 2:

   \( 1200 \div 2 = 600 \)

2. Continue dividing by 2:

   \( 600 \div 2 = 300 \)

3. Divide by 2 again:

   \( 300 \div 2 = 150 \)

4. Divide by 2 once more:

   \( 150 \div 2 = 75 \)

5. Now switch to the next smallest prime number, which is 3:

   \( 75 \div 3 = 25 \)

6. Next, divide by 5 (the next prime number):

   \( 25 \div 5 = 5 \)

7. Finally, divide by 5 once more:

   \( 5 \div 5 = 1 \)

Now we can summarize the prime factorization:

• The prime factorization is:

  \( 1200 = 2^4 \times 3^1 \times 5^2 \)

Thus, the prime factorization of 1200 as a product of prime numbers with exponents is:

\[ 1200 = 2^4 \times 3^1 \times 5^2 \]