Question

The number 100 expressed as a product of its prime factors is
4x5^2
10^2
2^2x25
2^2x5^2
Answer
Express 80 is a product of prime numbers with exponents
2^5x 5
2^4x5
2^3x10
2^3x 5
Answer
Xpress 120 as a product of prime numbers with exponents
Answer
Express 2x3^2x7 as a whole number
Answered by GPT-4o mini
To express the number 100 as a product of its prime factors, we first find its prime factorization.

100 can be broken down as follows:

1. Start with the number 100:
\[
100 = 10 \times 10
\]

2. Factor each 10:
\[
10 = 2 \times 5
\]

3. Therefore:
\[
100 = (2 \times 5) \times (2 \times 5) = 2^2 \times 5^2
\]

So, the correct expression of 100 as a product of its prime factors is:
\[
2^2 \times 5^2
\]

Thus, the correct option from your list is:
\[
\text{2}^2 \times 5^2
\]
Answered by GPT-4o mini
To express the number 80 as a product of its prime factors, we can follow these steps:

1. Start with the number 80.
\[
80 = 8 \times 10
\]

2. Factor each part:
- \(8 = 2^3\)
- \(10 = 2 \times 5\)

3. Now combine these factors:
\[
80 = 2^3 \times (2 \times 5) = 2^3 \times 2^1 \times 5
\]

4. Combine the like terms:
\[
80 = 2^{3+1} \times 5 = 2^4 \times 5
\]

Therefore, the correct expression of 80 as a product of prime factors with exponents is:
\[
2^4 \times 5
\]

So, the correct option from your list is:
\[
\text{2}^4 \times 5
\]
Answered by GPT-4o mini
To express the number 120 as a product of its prime factors with exponents, we can follow these steps:

1. Start with the number 120 and find its prime factorization:
- Divide by the smallest prime number, which is 2.
\[
120 \div 2 = 60
\]
- Divide 60 by 2 again:
\[
60 \div 2 = 30
\]
- Divide 30 by 2 again:
\[
30 \div 2 = 15
\]
- Now 15 is not divisible by 2, so we move to the next prime number, which is 3:
\[
15 \div 3 = 5
\]
- Finally, 5 is a prime number.

2. Now we can write the prime factorization:
- From the divisions, we see that:
\[
120 = 2^3 \times 3^1 \times 5^1
\]

Therefore, the expression of 120 as a product of prime numbers with exponents is:
\[
2^3 \times 3^1 \times 5^1
\]

This can also be written as:
\[
2^3 \times 3 \times 5
\]
Answered by GPT-4o mini
To express \(2 \times 3^2 \times 7\) as a whole number, follow these steps:

1. Calculate \(3^2\):
\[
3^2 = 3 \times 3 = 9
\]

2. Now substitute back into the expression:
\[
2 \times 9 \times 7
\]

3. Multiply \(2\) and \(9\):
\[
2 \times 9 = 18
\]

4. Now multiply \(18\) and \(7\):
\[
18 \times 7 = 126
\]

Thus, the expression \(2 \times 3^2 \times 7\) as a whole number is:
\[
\boxed{126}
\]