Final answer:
The correct expression of 48 as a product of prime numbers using exponents is 2⁴ × 3. This is found by repeatedly dividing 48 by 2 until we are left with a prime number, which is 3 in this case.
Step-by-step explanation:
To express 48 as a product of prime numbers using exponents, we need to find the prime factorization of 48. First, we divide 48 by the smallest prime number possible, which is 2, and we continue factoring until we are only left with prime numbers.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3 (which is a prime number)
Thus, we have factored 48 as 2 × 2 × 2 × 2 × 3, which simplifies to 2⁴ × 3 using exponents. Therefore, the correct expression of 48 as a product of prime numbers using exponents is 2⁴ × 3, which corresponds to option 3 in the question provided. None of the other options correctly represent the prime factorization of 48.