Simplify : `(3^2)^3`.

Answer

To simplify the expression \((3^2)^3\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

### Step-by-Step Solution:

1. **Identify the Base and Exponents**:
The base is \(3\), and the exponents are \(2\) and \(3\).

2. **Apply the Exponent Rule**:
Using the property \((a^m)^n = a^{m \cdot n}\), we can rewrite the expression:
\[ (3^2)^3 = 3^{2 \cdot 3} \]

3. **Calculate the New Exponent**:
Now, calculate \(2 \cdot 3\):
\[ 2 \cdot 3 = 6 \]
So, we have:
\[ (3^2)^3 = 3^6 \]

4. **Calculate \(3^6\)**:
Now we need to evaluate \(3^6\). This can be calculated as:
\[ 3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \]

5. **Perform the Multiplication**:
- First, calculate \(3 \times 3 = 9\).
- Next, calculate \(9 \times 3 = 27\).
- Then, calculate \(27 \times 3 = 81\).
- Finally, calculate \(81 \times 3 = 243\).

6. **Final Result**:
Therefore, \(3^6 = 729\).

### Final Answer:
\[ (3^2)^3 = 729 \]