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To simplify the expression \((4x^2)^3\), follow these steps:

1. Apply the power of a product rule, which states \((ab)^n = a^n \cdot b^n\).
   - Here, \(a = 4\) and \(b = x^2\), and \(n = 3\).

2. Apply the exponent to each part:
   \[
   (4x^2)^3 = 4^3 \cdot (x^2)^3
   \]

3. Simplify each term:
   \[
   4^3 = 64 \quad \text{and} \quad (x^2)^3 = x^{2 \cdot 3} = x^6
   \]

4. Combine the results:
   \[
   (4x^2)^3 = 64x^6
   \]

Thus, the simplified expression is:

\[
64x^6
\]

Would you like more details or explanations? 

Here are some related questions:

1. How would you simplify \((3x^3)^2\)?
2. What is the general rule for simplifying \((a^m)^n\)?
3. Can you simplify \((5xy)^4\)?
4. How do you simplify expressions with multiple variables, like \((2x^3y)^2\)?
5. What is the next step if you had a coefficient in front of \((4x^2)^3\), like \(2(4x^2)^3\)?

**Tip:** When simplifying expressions with exponents, always apply the exponent to both the coefficient and the variable separately!

Learn how to simplify the algebraic expression (4x^2)^3 step-by-step using exponent rules. This problem focuses on applying the power of a product rule and simplifying powers. Suitable for students in Grades 7-9.

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