Express the following numbers using exponential notation :
512

Answer

To express the number 512 using exponential notation, we will follow these steps:

### Step 1: Factor the number 512
We start by finding the prime factors of 512. We can do this by dividing the number 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

Now we have divided 512 down to 1 using the prime factor 2.

### Step 2: Count the number of times we used the factor 2
From the division, we see that we divided by 2 a total of 9 times. Therefore, we can express 512 as:

\[ 512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \]

### Step 3: Write in exponential notation
Since we multiplied 2 by itself 9 times, we can express this in exponential notation:

\[ 512 = 2^9 \]

### Final Answer
Thus, the exponential notation for the number 512 is:

\[ 512 = 2^9 \]

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