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: \[ 192 = 2^6 \times 3^1 \]