What is the prime factorization of 48 in exponential form?

To find the prime factorization of 48, we start by dividing it by the smallest prime number, which is 2.

1. Divide 48 by 2:

• 48 ÷ 2 = 24

2. Divide 24 by 2:

• 24 ÷ 2 = 12

3. Divide 12 by 2:

• 12 ÷ 2 = 6

4. Divide 6 by 2:

• 6 ÷ 2 = 3

5. Now, we cannot divide 3 by 2 anymore, so we move to the next prime number, which is 3:

• 3 ÷ 3 = 1

This gives us the prime factors of 48: four 2’s and one 3. In exponential form, we write the prime factorization as:

2⁴ × 3¹

Thus, the prime factorization of 48 in exponential form is 2⁴ × 3¹.