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

Question

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

Answer 1

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.