Express the following in exponential form
360

Answer

To express 360 in exponential form, we will follow these steps:

### Step 1: Prime Factorization
We need to find the prime factors of 360. We start by dividing 360 by the smallest prime number, which is 2.

- **Divide by 2:**
- 360 ÷ 2 = 180
- **Divide by 2 again:**
- 180 ÷ 2 = 90
- **Divide by 2 again:**
- 90 ÷ 2 = 45

Now, 45 cannot be divided by 2, so we move to the next smallest prime number, which is 3.

- **Divide by 3:**
- 45 ÷ 3 = 15
- **Divide by 3 again:**
- 15 ÷ 3 = 5

Now, we have reached 5, which is a prime number.

### Step 2: Count the Prime Factors
Now we will count how many times each prime factor appears in the factorization:

- The prime factor 2 appears **3 times** (from 360 to 180 to 90).
- The prime factor 3 appears **2 times** (from 45 to 15).
- The prime factor 5 appears **1 time** (just 5).

### Step 3: Write in Exponential Form
Now we can express 360 in exponential form using the counts of the prime factors:

- \( 360 = 2^3 \times 3^2 \times 5^1 \)

### Final Answer
Thus, the exponential form of 360 is:
\[ 2^3 \times 3^2 \times 5^1 \]

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