Simplify and express as the power 3, `(2^(4)xx2^(5)div2^(9))xx(729)^2`.

Answer

To simplify the expression \( (2^4 \times 2^5 \div 2^9) \times (729)^2 \) and express it as a power of 3, we can follow these steps:

### Step-by-Step Solution:

1. **Simplify the Division**:
We start with the division part of the expression. According to the exponent rules, when dividing powers with the same base, we subtract the exponents:
\[ 2^4 \times 2^5 \div 2^9 = 2^{4 + 5 - 9} \]
This simplifies to:
\[ 2^{4 + 5 - 9} = 2^{9 - 9} = 2^0 = 1 \]

**Hint**: Remember that \( a^0 = 1 \) for any non-zero \( a \).

2. **Simplify the Expression**:
Now, we have:
\[ 1 \times (729)^2 = (729)^2 \]

**Hint**: Multiplying by 1 does not change the value of the expression.

3. **Express 729 as a Power of 3**:
We know that:
\[ 729 = 3^6 \]
Therefore:
\[ (729)^2 = (3^6)^2 \]

**Hint**: Use the power of a power rule, which states \( (a^m)^n = a^{m \cdot n} \).

4. **Apply the Power of a Power Rule**:
Now we can simplify:
\[ (3^6)^2 = 3^{6 \times 2} = 3^{12} \]

**Hint**: When multiplying exponents, simply multiply the exponents together.

### Final Answer:
Thus, the expression simplifies to:
\[ 3^{12} \]