Express the prime factorization of 1,200 as a product of prime numbers with exponents. (2 points) ___4 . ___ . ___2=1,200

Answer 1

To express the prime factorization of 1,200, we start by dividing it by the smallest prime number and continue dividing until we reach 1.

Here’s the step-by-step factorization:

1. Divide by 2:
   • \( 1200 ÷ 2 = 600 \)
   • \( 600 ÷ 2 = 300 \)
   • \( 300 ÷ 2 = 150 \)
   • \( 150 ÷ 2 = 75 \) (at this point we can no longer divide by 2 since 75 is odd)

So we have factored out \( 2^4 \) (since we divided by 2 four times).

2. Now divide by 3:
   • \( 75 ÷ 3 = 25 \)

So we have accounted for \( 3^1 \).

3. Now divide by 5:
   • \( 25 ÷ 5 = 5 \)
   • \( 5 ÷ 5 = 1 \)

So we have accounted for \( 5^2 \).

Putting that all together, the prime factorization of 1,200 is: \[ 1200 = 2^4 \times 3^1 \times 5^2. \]

So expressed as a product of prime numbers with exponents, the answer is: \[ 2^4 \cdot 3^1 \cdot 5^2 = 1,200. \]