Express each of the following as a product of prime factors only in exponential form:

`729xx64`

Answer

To express \( 729 \times 64 \) as a product of prime factors in exponential form, we will break down each number into its prime factors step by step.

### Step 1: Factor 729
1. Start by dividing 729 by the smallest prime number, which is 3.
- \( 729 \div 3 = 243 \)
2. Divide 243 by 3.
- \( 243 \div 3 = 81 \)
3. Divide 81 by 3.
- \( 81 \div 3 = 27 \)
4. Divide 27 by 3.
- \( 27 \div 3 = 9 \)
5. Divide 9 by 3.
- \( 9 \div 3 = 3 \)
6. Finally, divide 3 by 3.
- \( 3 \div 3 = 1 \)

Counting the number of times we divided by 3, we see that we divided 6 times. Therefore, we can express 729 as:
\[ 729 = 3^6 \]

### Step 2: Factor 64
1. Start by dividing 64 by the smallest prime number, which is 2.
- \( 64 \div 2 = 32 \)
2. Divide 32 by 2.
- \( 32 \div 2 = 16 \)
3. Divide 16 by 2.
- \( 16 \div 2 = 8 \)
4. Divide 8 by 2.
- \( 8 \div 2 = 4 \)
5. Divide 4 by 2.
- \( 4 \div 2 = 2 \)
6. Finally, divide 2 by 2.
- \( 2 \div 2 = 1 \)

Counting the number of times we divided by 2, we see that we divided 6 times. Therefore, we can express 64 as:
\[ 64 = 2^6 \]

### Step 3: Combine the Results
Now we can express the original expression \( 729 \times 64 \) using the prime factorization we found:
\[ 729 \times 64 = 3^6 \times 2^6 \]

### Final Answer
Thus, the expression \( 729 \times 64 \) as a product of prime factors in exponential form is:
\[ 3^6 \times 2^6 \]

---