Express the following in exponential form.
`512`

Answer

To express the number 512 in exponential form, we need to find its prime factorization. Let's break it down step by step.

### Step 1: Identify the prime factors of 512
We start dividing 512 by the smallest prime number, which is 2.

- 512 ÷ 2 = 256
- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

### Step 2: Count the number of times we divided by 2
From the steps above, we divided by 2 a total of 9 times until we reached 1.

### Step 3: Write the result in exponential form
Since we divided by 2 a total of 9 times, we can express 512 as:
\[ 512 = 2^9 \]

### Final Answer
Thus, the exponential form of 512 is \( 2^9 \).

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