Question

Rewrite 192 as a product of its prime factors using exponents.(1 point) Responses 82 · 3 8 squared · 3 2 · 2 · 2 · 2 · 2 · 2 · 3 2 · 2 · 2 · 2 · 2 · 2 · 3 26 · 3 2 to the 6th power · 3 4 · 48

Answer 1

To rewrite 192 as a product of its prime factors using exponents, we first factor it into its prime components.

Starting with 192:
1. Divide by 2:
- 192 ÷ 2 = 96
2. Divide by 2 again:
- 96 ÷ 2 = 48
3. Divide by 2 again:
- 48 ÷ 2 = 24
4. Divide by 2 again:
- 24 ÷ 2 = 12
5. Divide by 2 again:
- 12 ÷ 2 = 6
6. Divide by 2 one more time:
- 6 ÷ 2 = 3
7. Now we are left with 3, which is a prime number.

Counting the factors of 2, we have:
- Six 2's, which can be expressed as \(2^6\).

We also have one 3:
- One 3, which can be expressed as \(3^1\).

Combining these, we write 192 as:
\[
192 = 2^6 \times 3^1
\]

So, the final response is:
\[
192 = 2^6 \times 3^1
\]