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

Blank to the forth power blank blank to the second power

7 answers

To find the prime factorization of 1,200, we can break it down step by step.

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

    • \( 1200 \div 2 = 600 \)
    • \( 600 \div 2 = 300 \)
    • \( 300 \div 2 = 150 \)
    • \( 150 \div 2 = 75 \)

    We’ve divided by 2 four times, so we have \( 2^4 \).

  2. Next, we divide 75 by the next smallest prime, which is 3:

    • \( 75 \div 3 = 25 \)

    We’ve divided by 3 once, so we have \( 3^1 \).

  3. Now we factor 25, which is a power of the next smallest prime, 5:

    • \( 25 \div 5 = 5 \)
    • \( 5 \div 5 = 1 \)

    We’ve divided by 5 two times, so we have \( 5^2 \).

Now, putting it all together, the prime factorization of 1,200 can be expressed as: \[ 1,200 = 2^4 \times 3^1 \times 5^2 \]

Therefore, filling in the blanks with the appropriate primes and exponents, we get:

Blank to the fourth power (2⁴) blank (3¹) blank to the second power (5²).

So the answer is what

The prime factorization of 1,200 expressed as a product of prime numbers with exponents is:

2 to the fourth power (2⁴), 3 to the first power (3¹), 5 to the second power (5²).

In the format you specified, it would be:

2^4 3^1 5^2.

If you need just the exponents and corresponding primes for your blanks:

  • Blank to the fourth power: 2
  • Blank to the second power: 5

So your final answer is:

2 to the fourth power, 3 to the first power, and 5 to the second power.

3 has no power

Apologies for any confusion. You are correct; in the context where prime numbers are expressed with exponents, 3 does not have a power in the prime factorization of 1,200.

The corrected prime factorization of 1,200, emphasizing that the power of 3 is 1 (which is often omitted in written forms), is:

\[ 1,200 = 2^4 \times 3^1 \times 5^2 \]

For filling out your blanks based on your original request:

  • Blank to the fourth power: 2
  • Blank: (this can be interpreted as the prime number 3, but it doesn't have a power)
  • Blank to the second power: 5

So the completed expression reflecting what was originally requested would be:

2 to the fourth power, 3 (implicitly to the first power), and 5 to the second power.

In summary:

  • 2 to the fourth power
  • 3
  • 5 to the second power

If the context does not allow for the base number "3" without an exponent, please fill in the blanks according to the format as you see fit. Thank you!

Can you give me all the answers to the unit 6 test
PLZ!!!!!!!!!!!!!!!!!!!!!!!$$$

I’m sorry, but I can’t assist with that. If you have questions about specific topics or concepts from your Unit 6 test, I'd be happy to help explain those!