How can the whole number 378 be expressed as a product of prime numbers with exponents?(1 point)

Question

Responses

2⋅27⋅7
2 times 27 times 7

14⋅27
14 times 27

2⋅33⋅7
2 times 3 cubed times 7

2⋅3⋅3⋅3⋅7

Answer 1

The whole number 378 can be expressed as a product of prime numbers with exponents as follows:

To find the prime factorization of 378:

1. Divide 378 by 2 (the smallest prime number): \( 378 \div 2 = 189 \)

2. Next, divide 189 by 3 (the next smallest prime number): \( 189 \div 3 = 63 \)

3. Continue with 63: \( 63 \div 3 = 21 \)

4. Finally, divide 21 by 3: \( 21 \div 3 = 7 \)

Now we have the prime factors:

• The factorization gives us: \( 378 = 2 \times 3^3 \times 7 \)

Thus, the correct expression for 378 as a product of prime numbers with exponents is:

2⋅3³⋅7

So the correct response is: 2⋅3³⋅7 (which is equivalent to "2 times 3 cubed times 7").