Question

Express 48 as a product of prime numbers using exponents

3 x 4^2
2^2 x 3 x 4
2^4 x 3
2 x 3 x 2^3

Answer 1

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

Starting with the prime factorization:

1. Divide 48 by 2 (the smallest prime number):
\[
48 \div 2 = 24
\]
2. Continue dividing by 2:
\[
24 \div 2 = 12
\]
3. Again divide by 2:
\[
12 \div 2 = 6
\]
4. And once more:
\[
6 \div 2 = 3
\]
5. Finally, 3 is a prime number.

Now we can record the factors:
\[
48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3^1
\]

Thus, \(48\) can be expressed as:
\[
2^4 \times 3
\]

So the correct expression for 48 as a product of prime numbers using exponents is:
\[
\boxed{2^4 \times 3}
\]

Among the options you provided, \(2^4 \times 3\) matches none directly, but it is the correct prime factorization of 48.