https://file.aiquickdraw.com/mathbot/file/17374188097159z1evcpq.jpg

Let's break down the expression in the image: 

You are asked to simplify:

\[
(4x^2)^3 + 7x^6
\]

Step-by-step:

1. **Expand \( (4x^2)^3 \)**:
   - Use the power of a power rule: \( (a^m)^n = a^{m \times n} \).
   - Here, we have \( (4x^2)^3 \), which means:
   \[
   4^3 \times (x^2)^3 = 64x^6
   \]

2. **Now, simplify the full expression**:
   \[
   64x^6 + 7x^6
   \]
   - Since both terms have \( x^6 \), factor out \( x^6 \):
   \[
   (64 + 7)x^6 = 71x^6
   \]

So the simplified expression is \( 71x^6 \).

Therefore, the correct answer is: **71x^6**.

Would you like further details on any of these steps, or do you have any questions?

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Here are 5 follow-up questions that may interest you:
1. How do you apply the power of a product rule in algebra?
2. What is the difference between adding and multiplying exponents?
3. Can you simplify expressions like \( (2x^3)^4 \)?
4. How do you factor out common terms in algebraic expressions?
5. What happens if the powers of the variables are different in an expression like \( x^2 + x^3 \)?

Tip: When simplifying powers, always check whether the terms have the same base and exponent to combine them.

Learn how to simplify the expression (4x^2)^3 + 7x^6 step-by-step. This problem involves exponentiation and simplifying polynomials, suitable for students in Grades 8-9.

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