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

Question

Responses

2⋅3⋅3⋅3⋅7
2 times 3 times 3 times 3 times 7

14⋅27
14 times 27

2⋅33⋅7
2 times 3 cubed times 7

2⋅27⋅7

Answer 1

To express the whole number 378 as a product of prime numbers with exponents, we first need to factor it.

1. Start by dividing 378 by the smallest prime number, which is 2:
   \( 378 ÷ 2 = 189 \)
   So, we have \( 2 \) as one of the prime factors.

2. Next, we factor 189. The sum of the digits of 189 (1 + 8 + 9 = 18) is divisible by 3, so we can divide by 3:
   \( 189 ÷ 3 = 63 \)
   Now, we have \( 3 \) as a factor.

3. Then, we factor 63 by dividing by 3 again:
   \( 63 ÷ 3 = 21 \)
   We now have another \( 3 \) as a factor.

4. Finally, we factor 21 by dividing by 3 one more time:
   \( 21 ÷ 3 = 7 \)
   So, we have another \( 3 \) and \( 7 \) as a factor.

Putting it all together, we have:
\( 378 = 2 × 3 × 3 × 3 × 7 \)
or in exponential form, \( 378 = 2^1 × 3^3 × 7^1 \).

Among the provided responses, the correct expression of 378 as a product of prime numbers with exponents is:

2⋅3³⋅7 (2 times 3 cubed times 7).