Question
How can the whole number 378 be expressed as a product of prime numbers with exponents?(1 point)
Responses
14⋅27
14 times 27
2⋅3⋅3⋅3⋅7
2 times 3 times 3 times 3 times 7
2⋅33⋅7
2 times 3 cubed times 7
2⋅27⋅7
Responses
14⋅27
14 times 27
2⋅3⋅3⋅3⋅7
2 times 3 times 3 times 3 times 7
2⋅33⋅7
2 times 3 cubed times 7
2⋅27⋅7
Answers
GPT-4o mini
To express the whole number 378 as a product of prime numbers with exponents, we first need to perform the prime factorization of 378.
1. Start by dividing 378 by 2 (the smallest prime number):
\[
378 \div 2 = 189
\]
2. Next, we factor 189. Since 189 is odd, we divide by the next smallest prime number, which is 3:
\[
189 \div 3 = 63
\]
3. We continue factoring 63, and again use 3:
\[
63 \div 3 = 21
\]
4. Next, we factor 21 using 3:
\[
21 \div 3 = 7
\]
5. Finally, we are left with 7, which is a prime number.
Putting it all together, we have:
\[
378 = 2 \times 3 \times 3 \times 3 \times 7
\]
This can also be expressed using exponents:
\[
378 = 2^1 \times 3^3 \times 7^1
\]
Therefore, the correct response that expresses 378 as a product of prime numbers with exponents is:
**2⋅3³⋅7**.
1. Start by dividing 378 by 2 (the smallest prime number):
\[
378 \div 2 = 189
\]
2. Next, we factor 189. Since 189 is odd, we divide by the next smallest prime number, which is 3:
\[
189 \div 3 = 63
\]
3. We continue factoring 63, and again use 3:
\[
63 \div 3 = 21
\]
4. Next, we factor 21 using 3:
\[
21 \div 3 = 7
\]
5. Finally, we are left with 7, which is a prime number.
Putting it all together, we have:
\[
378 = 2 \times 3 \times 3 \times 3 \times 7
\]
This can also be expressed using exponents:
\[
378 = 2^1 \times 3^3 \times 7^1
\]
Therefore, the correct response that expresses 378 as a product of prime numbers with exponents is:
**2⋅3³⋅7**.