Express 48 as a product of prime numbers using exponents.
To express 48 as a product of prime numbers using exponents, we can start by dividing 48 by the smallest prime number, which is 2.
48 ÷ 2 = 24
Now we divide 24 by 2 again:
24 ÷ 2 = 12
We keep dividing by 2 until we can't anymore:
12 ÷ 2 = 6
6 ÷ 2 = 3
Now we are left with 3, which is a prime number itself. Therefore, the prime factorization of 48 using exponents is:
2² × 3 × 3
Simplifying this, we get:
2² × 3²
To express 48 as a product of prime numbers using exponents, we need to find the prime factorization of 48.
Step 1: Find the smallest prime number that divides 48. In this case, it is 2 because 48 is divisible by 2.
48 ÷ 2 = 24
Step 2: Repeat step 1 with the quotient.
24 ÷ 2 = 12
Step 3: Continue dividing by the smallest prime number until you reach a prime number.
12 ÷ 2 = 6
Step 4: Divide by the next smallest prime (3).
6 ÷ 3 = 2
Step 5: Divide by the remaining number (2).
2 ÷ 2 = 1
Step 6: Once you reach 1, stop dividing. The prime factors of 48 are 2, 2, 2, and 2.
Therefore, we can express 48 as a product of prime numbers using exponents as:
48 = 2^4