Let's simplify the expression step by step:

Given expression: $\left(2xy\right)^2 \left(-3x^2\right) \left(4y^2\right)$

Step 1: Expand $(2xy)^2$

We start by applying the exponent to each term inside the parentheses: $(2xy)^2 = 2^2 \cdot x^2 \cdot y^2 = 4x^2y^2$

Step 2: Multiply the terms

Now we multiply the three terms: $(4x^2y^2) \cdot (-3x^2) \cdot (4y^2)$

First, combine the constants: $4 \cdot (-3) \cdot 4 = -48$

Next, multiply the powers of $x$ and $y$: $x^2 \cdot x^2 = x^{2+2} = x^4$ $y^2 \cdot y^2 = y^{2+2} = y^4$

Step 3: Final expression

Now, put everything together: $-48x^4y^4$

Thus, the simplified expression is: $\boxed{-48x^4y^4}$

Would you like further clarification on any part of the solution?

Here are some related questions for further practice:

1. How do you handle negative exponents when simplifying expressions?
2. What happens if we add exponents of the same base in multiplication?
3. How do you simplify expressions with more than two variables?
4. How would the result change if the exponent of $x$ was different?
5. Can we simplify the expression if there were fractions involved?

Tip: When simplifying powers, always apply the exponent to each factor in parentheses and combine like terms in the multiplication phase.