Question

Express the prime factorization of 1,200 as a product of prime numbers with exponents.(2 points)
blank to the power of 4 dot in the middle blank dot in the middle blank to the power of 2 =1,200

Answer 1

To express the prime factorization of 1,200, we first break it down into its prime factors.

1. Start by dividing by 2 (the smallest prime number):
- 1200 ÷ 2 = 600
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75

2. Now, divide by 3 (the next smallest prime number):
- 75 ÷ 3 = 25

3. Finally, divide by 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So, the prime factorization of 1,200 can be collected as:
- \( 2^4 \) (since 2 was used 4 times)
- \( 3^1 \) (since 3 was used once)
- \( 5^2 \) (since 5 was also used 2 times)

Putting this all together, the prime factorization of 1,200 is:
\[ 2^4 \cdot 3^1 \cdot 5^2 \]

Thus, the answer is:
\[ 2^4 \cdot 3^1 \cdot 5^2 = 1200 \]