Express each of the following as a product of prime factors only in exponential form:

768

Answer

To express 768 as a product of prime factors in exponential form, we will follow these steps:

### Step 1: Divide by the smallest prime number
We start with 768 and divide it by the smallest prime number, which is 2.

768 ÷ 2 = 384

### Step 2: Continue dividing by 2
We continue dividing by 2 until we can no longer divide evenly.

384 ÷ 2 = 192
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3

### Step 3: Count the number of times we divided by 2
We divided by 2 a total of 8 times.

### Step 4: Identify the remaining factor
After dividing down to 3, we see that 3 is a prime number and can be counted as one factor.

### Step 5: Write the prime factorization
Now we can express 768 as a product of its prime factors:

768 = 2^8 × 3^1

### Final Answer
Thus, the prime factorization of 768 in exponential form is:

**768 = 2^8 × 3^1**

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