Express the following in exponential form.
`729`

Answer

To express the number 729 in exponential form, we need to factor it into its prime factors and then write it in the form of \( A^n \), where \( A \) is the base and \( n \) is the exponent.

### Step-by-Step Solution:

1. **Find the Prime Factors of 729:**
- Start dividing 729 by the smallest prime number, which is 3.
- \( 729 \div 3 = 243 \)
- \( 243 \div 3 = 81 \)
- \( 81 \div 3 = 27 \)
- \( 27 \div 3 = 9 \)
- \( 9 \div 3 = 3 \)
- \( 3 \div 3 = 1 \)

So, the prime factorization of 729 is:
\[ 729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \]

2. **Count the Number of Times the Prime Factor Appears:**
- From the factorization, we see that 3 appears 6 times.

3. **Write in Exponential Form:**
- Since 3 is the base and it appears 6 times, we can express 729 in exponential form as:
\[ 729 = 3^6 \]

### Final Answer:
\[ 729 = 3^6 \]