Express the following in exponential form.
1296

Answer

To express the number 1296 in exponential form, we will follow these steps:

### Step 1: Find the Prime Factorization of 1296
We start by dividing 1296 by the smallest prime number, which is 2, and continue dividing until we can no longer divide evenly.

1. **Divide by 2**:
- 1296 ÷ 2 = 648
- 648 ÷ 2 = 324
- 324 ÷ 2 = 162
- 162 ÷ 2 = 81 (81 is not divisible by 2)

2. **Now divide by 3** (the next smallest prime):
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

### Step 2: Write the Prime Factorization
From the divisions, we find:
- The number 2 appears 4 times.
- The number 3 appears 4 times.

Thus, we can express 1296 as:
\[ 1296 = 2^4 \times 3^4 \]

### Step 3: Combine the Factors
Since both factors have the same exponent, we can combine them:
\[ 1296 = (2 \times 3)^4 \]

### Step 4: Simplify the Base
Now, we calculate the base:
\[ 2 \times 3 = 6 \]
Thus, we can rewrite the expression as:
\[ 1296 = 6^4 \]

### Final Answer
Therefore, the exponential form of 1296 is:
\[ \boxed{6^4} \]

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