Express 120 as a product of prime numbers with exponents.
A. 2^3 x 3 x 5^2
B. 2^3 x 3 x 5
C. 2^3 x 3^2 x 5
D. 2^2 x 3^2 x 5
To express 120 as a product of prime numbers with exponents, we need to find the prime factors of 120 and write them in their prime factorization form.
One way to find the prime factors of a number is to start with the smallest prime number, which is 2, and divide the number by 2 as many times as possible. If the number can no longer be divided evenly by 2, move on to the next prime number, which is 3. Repeat this process until the number cannot be divided any further.
Let's break it down step by step:
1. Divide 120 by 2: 120 ÷ 2 = 60
2. Divide 60 by 2 again: 60 ÷ 2 = 30
3. Divide 30 by 2 one more time: 30 ÷ 2 = 15
4. Now, 15 is not divisible by 2 anymore, so we move on to the next prime number, which is 3.
Divide 15 by 3: 15 ÷ 3 = 5
We have found all the prime factors of 120: 2, 2, 2, 3, and 5.
To express it as a product of prime numbers with exponents, we can group them together:
2 × 2 × 2 × 3 × 5
Simplifying this, we get:
2^3 × 3 × 5
Therefore, the answer is A. 2^3 × 3 × 5^2.
Prime Factorization Quick Check
1. 41
2. 51
3. {1, 3, 9, 27, 81}
4. 2⁴ × 3
5. 2³ × 3 × 5