Question

Question

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

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

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

23 × 3 × 5
2 cubed times 3 times 5

22 × 32 × 5

Answer 1

To express 120 as a product of prime numbers with exponents, we first need to perform the prime factorization of 120.

1. Start by dividing by the smallest prime number, which is 2:

   • 120 ÷ 2 = 60
   • 60 ÷ 2 = 30
   • 30 ÷ 2 = 15

   So far, we have \(2^3\) (since we divided by 2 three times).

2. Now we are left with 15, which is not divisible by 2, so we move to the next prime number, which is 3:

   • 15 ÷ 3 = 5

   Now we have \(3^1\) (since we divided by 3 once).

3. Finally, we are left with 5, which is a prime number itself.

Putting it all together, we have: \[ 120 = 2^3 \times 3^1 \times 5^1 \]

This can be written more concisely as: \[ 120 = 2^3 \times 3 \times 5 \]

Thus, the correct response is: \(2^3 \times 3 \times 5\) (which corresponds to \(2^3 \times 3^1 \times 5^1\)). The notation often omits the exponent of 1 for clarity.

Among the given responses, the correct one is: \(2^3 \times 3 \times 5\)