Question

Express 48 as a product of prime numbers using exponents A 2 x 2 x 2 x 2 x 3 B 2 x 3 x 2 x 2 x 2 C 2 x 2 x 3 x 4 D 3 x 4 x 4

Answer 1

To express 48 as a product of prime numbers using exponents, we first need to find its prime factorization.

Let's break down 48:

1. Divide 48 by 2 (the smallest prime number):
- 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. Finally, 3 is a prime number.

So, we have:
\[
48 = 2^4 \times 3^1
\]

From the provided choices for expressing 48, we see:
- A: \( 2 \times 2 \times 2 \times 2 \times 3 \) can be expressed as \( 2^4 \times 3 \)
- B: \( 2 \times 3 \times 2 \times 2 \times 2 \) can also be rearranged as \( 2^4 \times 3 \)
- C: \( 2 \times 2 \times 3 \times 4 \) includes \( 4 \), which is not prime.
- D: \( 3 \times 4 \times 4 \) includes \( 4 \), which is also not prime.

Therefore, the correct representations that can express 48 as a product of prime numbers using exponents are A and B.