It seems like you have an expression here that needs simplification. Let’s break it down:

The given expression is:

$4x - 3y^2(2x^2y^3)^4$

Step 1: Expand the second term

The second term $(2x^2y^3)^4$ involves raising both $x^2$ and $y^3$ to the power of 4. Using the power of a product rule $(ab)^n = a^n b^n$, we can simplify it:

$(2x^2y^3)^4 = 2^4 (x^2)^4 (y^3)^4$

This simplifies further to:

$16x^8y^{12}$

Step 2: Multiply the terms

Now, we substitute this result back into the original expression:

$4x - 3y^2(16x^8y^{12})$

Distribute $3y^2$ to the terms inside the parentheses:

$4x - 48x^8y^{14}$

Final Result:

$4x - 48x^8y^{14}$

So, the simplified expression is:

$4x - 48x^8y^{14}$

Would you like further details on any of these steps?

Here are some related questions:

1. What happens when you raise a product to a power in algebraic expressions?
2. Can you apply the distributive property to simplify more complex expressions?
3. How would you simplify a polynomial with multiple terms like this?
4. What is the power of a product rule in exponents?
5. How do you handle negative exponents in expressions like these?

Tip: When dealing with exponents, always separate terms with variables and constants to avoid errors during expansion.