Express the prime factorization of 1200 as a product of prime numbers with exponents

Answer 1

To express the prime factorization of 1200 as a product of prime numbers with exponents, we can follow these steps:

1. Start by dividing 1200 by the smallest prime number, which is 2.
2. Continue dividing by primes until we are left with 1.

Let's break down the factorization:

• \( 1200 \div 2 = 600 \)
• \( 600 \div 2 = 300 \)
• \( 300 \div 2 = 150 \)
• \( 150 \div 2 = 75 \)
• \( 75 \div 3 = 25 \)
• \( 25 \div 5 = 5 \)
• \( 5 \div 5 = 1 \)

Now we can count the number of times each prime factor is used:

• The prime number 2 is used 4 times.
• The prime number 3 is used 1 time.
• The prime number 5 is used 2 times.

Thus, we can express the prime factorization of 1200 as:

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