The expression in the image you've uploaded is:

$\frac{(3m^2n^2n)^2}{(2mn)(3m^2n)}$

To simplify this, let's first break down the terms.

Step 1: Simplify the powers

• The numerator: $(3m^2n^2n)^2$

  • Combine the powers of $n$: $n^2 \cdot n = n^3$
  • The numerator becomes $(3m^2n^3)^2 = 9m^4n^6$

• The denominator: $(2mn)(3m^2n)$

  • Multiply the constants and like terms: $2 \times 3 = 6$, $m \times m^2 = m^3$, $n \times n = n^2$
  • The denominator becomes $6m^3n^2$

Step 2: Divide the terms

Now the expression becomes:

$\frac{9m^4n^6}{6m^3n^2}$

Step 3: Simplify by canceling out common terms

• For $m$: $m^4/m^3 = m$
• For $n$: $n^6/n^2 = n^4$

The simplified expression is:

$\frac{9mn^4}{6}$

Step 4: Simplify the constants

$\frac{9}{6} = \frac{3}{2}$

Thus, the simplified expression is:

$\frac{3mn^4}{2}$

Do you need further clarification or have any specific questions about this problem?

Here are a few related questions that might help further your understanding:

1. How do you handle exponents in fractions?
2. What are the rules for simplifying expressions with variables and exponents?
3. Can you explain the process of multiplying and dividing powers of the same base?
4. How do you simplify complex algebraic expressions with multiple variables?
5. What is the importance of factoring when simplifying algebraic expressions?

Tip: When simplifying expressions, always look for common factors in both the numerator and denominator to cancel out first.