Express the following in exponential form
507

Answer

To express 507 in exponential form, we will follow these steps:

### Step 1: Prime Factorization
We need to factor 507 into its prime factors.

- First, we check if 507 is divisible by 2. Since 507 is an odd number, it is not divisible by 2.

- Next, we check divisibility by 3. We can do this by adding the digits of 507: \(5 + 0 + 7 = 12\), which is divisible by 3. Therefore, we divide 507 by 3:
\[ 507 \div 3 = 169 \]

### Step 2: Factor 169
Now we need to factor 169.

- We check if 169 is divisible by 3. The sum of the digits \(1 + 6 + 9 = 16\) is not divisible by 3, so we move on.

- Next, we check divisibility by 4, 5, and 6, and find that it is not divisible by any of these.

- Finally, we check divisibility by 13. We know that \(13 \times 13 = 169\), so:
\[ 169 = 13^2 \]

### Step 3: Combine the Factors
Now we combine the factors we found:
\[ 507 = 3 \times 169 = 3 \times 13^2 \]

### Step 4: Write in Exponential Form
We can express this in exponential form as:
\[ 507 = 3^1 \times 13^2 \]

### Final Answer
Thus, the exponential form of 507 is:
\[ 3^1 \times 13^2 \]

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