The problem is to simplify the expression $(3n^3 \cdot 2n^2)^2$.

1. Problem Description

The problem is to simplify the expression $(3n^3 \cdot 2n^2)^2$.

2. Solution Steps

First, simplify the expression inside the parenthesis by multiplying the terms:

$3n^3 \cdot 2n^2 = (3 \cdot 2) \cdot (n^3 \cdot n^2)$.

Then, multiply the coefficients and use the rule of exponents, $a^m \cdot a^n = a^{m+n}$, to simplify the variables.

$3 \cdot 2 = 6$

$n^3 \cdot n^2 = n^{3+2} = n^5$

Therefore, the expression inside the parenthesis becomes:

$3n^3 \cdot 2n^2 = 6n^5$.

Now, substitute this back into the original expression:

$(6n^5)^2$.

To simplify this, use the rule $(ab)^n = a^n b^n$ and $(a^m)^n = a^{m \cdot n}$:

$(6n^5)^2 = 6^2 \cdot (n^5)^2$.

Then, calculate $6^2$ and simplify $(n^5)^2$:

$6^2 = 36$

$(n^5)^2 = n^{5 \cdot 2} = n^{10}$.

Finally, substitute these back into the expression:

$6^2 \cdot (n^5)^2 = 36n^{10}$.

3. Final Answer

$36n^{10}$