Express 120 as a product of prime numbers with exponents.(1 point)
Responses
2^2 × 3^2 × 5
2^2 × 3 × 5^2
2^3 × 3^2 × 5
2^3 × 3 × 5
2^3 × 3 × 5
The correct expression for 120 as a product of prime numbers with exponents is:
2^3 × 3 × 5
To express 120 as a product of prime numbers with exponents, we need to find the prime factorization of 120. Here's how you can do it:
Step 1: Start by dividing 120 by the smallest prime number, which is 2. Since 120 is divisible by 2, we get 120 ÷ 2 = 60.
Step 2: Now, divide 60 by 2 again: 60 ÷ 2 = 30.
Step 3: Continue dividing by 2 until you can no longer divide evenly. In this case, 30 is also divisible by 2: 30 ÷ 2 = 15.
Step 4: Now, move on to the next prime number, which is 3. Divide 15 by 3: 15 ÷ 3 = 5.
Step 5: Finally, divide 5 by itself since it is a prime number: 5 ÷ 5 = 1.
Now, let's write the prime factorization of 120 using exponents:
2^3 × 3^1 × 5^1.
So, 120 can be expressed as a product of prime numbers with exponents as 2^3 × 3^1 × 5^1.