Express 120 as a product of prime numbers with exponents.(1 point)

Question

Responses

22 × 32 × 5
2 squared times 3 squared times 5

23 × 32 × 5
2 cubed times 3 squared times 5

22 × 3 × 52
2 squared times 3 times 5 squared

23 × 3 × 5

Answer 1

To express 120 as a product of prime numbers with exponents, we first need to factor 120 into its prime components.

1. Start with the number: 120
2. Divide by the smallest prime number, 2:
   • 120 ÷ 2 = 60
3. Divide 60 by 2:
   • 60 ÷ 2 = 30
4. Divide 30 by 2:
   • 30 ÷ 2 = 15
5. Now, divide 15 by the next smallest prime number, which is 3:
   • 15 ÷ 3 = 5
6. The remaining number, 5, is also a prime number.

Now, we can summarize the factorization:

• We divided by 2 three times (2 × 2 × 2), which is \(2^3\).
• We divided by 3 once, which is \(3^1\).
• Finally, we have 5 once, which is \(5^1\).

Therefore, the prime factorization of 120 is:

\[ 2^3 \times 3^1 \times 5^1 \]

In your response options, this can be expressed as:

\[ 2^3 \times 3 \times 5 \]

So, the correct answer would be:

\( 2^3 \times 3 \times 5 \)