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

Question

___^4 x ___ X ____^2=1,200

Answer 1

To find the prime factorization of 1,200, we start with dividing it by the smallest prime numbers.

1. Divide by 2:

   • $1200÷2=600$
   • $600÷2=300$
   • $300÷2=150$
   • $150÷2=75$ (At this point 75 isn't divisible by 2, we switch to the next prime number)

2. Divide by 3:

   • $75÷3=25$ (25 isn't divisible by 3, we switch to the next prime number)

3. Divide by 5:

   • $25÷5=5$
   • $5÷5=1$

Putting it all together, we have:

• From 2, we divided 4 times: $2^4$
• From 3, we used it once: $3^1$
• From 5, we divided 2 times: $5^2$

Thus, the prime factorization of 1,200 is: $$1,200=2^4\times 3^1\times 5^2$$

So, in the given format:

• $2^4\times 3^1\times 5^2=1,200$

Therefore, filling in the blanks: 2^4 x 3 x 5^2 = 1,200.