express 120 as a product of prime numbers using exponents
To express 120 as a product of prime numbers using exponents, we need to factorize 120 into its prime factors and rewrite it using exponents.
120 can be factored as follows:
120 = 2 × 60
= 2 × 2 × 30
= 2 × 2 × 2 × 15
= 2 × 2 × 2 × 3 × 5
So, in terms of prime factors with exponents, 120 can be expressed as:
120 = 2^3 × 3^1 × 5^1
express 2 x 3^2 x 7 as a whole number
To express the product 2 x 3^2 x 7 as a whole number, we need to simplify the expression.
2 x 3^2 x 7 = 2 x 9 x 7
Now, we can multiply the numbers together:
2 x 9 x 7 = 18 x 7
Multiplying 18 by 7, we get:
18 x 7 = 126
Therefore, 2 x 3^2 x 7 can be simplified to the whole number 126.
To express 120 as a product of prime numbers using exponents, we need to find all the prime factors of 120.
1. First, we start by dividing 120 by the smallest prime number, which is 2. We continue dividing by 2 until we cannot do so anymore:
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
So, we have found three 2's as prime factors of 120.
2. Next, we divide the remaining quotient, which is 15, by the next prime number, which is 3:
15 ÷ 3 = 5
We have found one 3 as a prime factor of 120.
3. Now, since 5 is a prime number itself, we cannot divide it further.
After this process, we have found all the prime factors of 120: 2, 2, 2, 3, and 5.
To express this as a product of prime numbers using exponents, we write it as:
2^3 × 3^1 × 5^1
Therefore, 120 can be expressed as 2 raised to the power 3 multiplied by 3 raised to the power 1 multiplied by 5 raised to the power 1.