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The problem states that the length of the rectangular field is \( 2x^2 \) and the width is \( 4x \). We are asked to find the area of the rectangular field.

### Step-by-Step Solution:
The area \( A \) of a rectangle is given by the formula:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the given values for length and width:
\[
A = (2x^2) \times (4x)
\]

Now, multiply the terms:
\[
A = 2x^2 \times 4x = 8x^3
\]

Thus, the area of the rectangular field is \( 8x^3 \).

### Correct Answer:
The correct option is \( 8x^3 \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the area formula change if both length and width were linear terms like \( ax + b \)?
2. What happens to the area if the length and width are doubled?
3. How do you simplify the product of two polynomials like \( (x^2)(x^3) \)?
4. If the width were instead \( 5x^2 \), how would the area change?
5. Can you find the perimeter of the rectangle given these dimensions?

**Tip:** When multiplying expressions with exponents, always add the exponents if the base is the same.

The length of a rectangular field is 2x^2 and the width is 4x. Find the area of the rectangular field.

Learn how to find the area of a rectangular field where the length is 2x^2 and the width is 4x. This problem demonstrates the use of algebra and exponent rules to calculate the area of geometric shapes. Suitable for Grades 7-9.

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