To simplify the expression \((3^3m^3n)^2\), follow these steps:

1. First, simplify the expression inside the parentheses:
   \[
   3^3m^3n = 27m^3n
   \]

2. Now, raise the entire expression inside the parentheses to the power of 2:
   \[
   (27m^3n)^2 = 27^2 \cdot (m^3)^2 \cdot n^2
   \]

3. Calculate each component:
   \[
   27^2 = 729
   \]
   \[
   (m^3)^2 = m^{6}
   \]
   \[
   n^2 = n^2
   \]

4. Combine everything together:
   \[
   (3^3m^3n)^2 = 729m^6n^2
   \]

So, the simplified expression is \(\boxed{729m^6n^2}\).

Would you like any further details or have any questions? 

Here are 5 related questions you might find useful:

1. How would you simplify \((4x^2y^3)^3\)?
2. What is the simplified form of \((2a^4b^2)^2\)?
3. How do you expand \((5x^3y^2)^2\)?
4. What is \((2^3x^4y)^2\) simplified to?
5. How would you simplify \((6mn^2p)^3\)?

**Tip:** When raising a product to a power, apply the exponent to each factor inside the parentheses.

Learn how to simplify the expression (3^3m^3n)^2 step-by-step with detailed explanations. This problem involves exponentiation and the simplification of exponential expressions. Suitable for students in Grades 7-9.

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