This phone is right to equivalent expressions for the area of the rectangle that has the sides of 7 to the second power and 4 to the second power

To find equivalent expressions for the area of a rectangle where the sides are \( 7^2 \) and \( 4^2 \), we follow these steps:

1. The formula for the area \( A \) of a rectangle is:
   \[
   A = \text{length} \times \text{width}
   \]

2. In this case, the length and width are \( 7^2 \) and \( 4^2 \), so:
   \[
   A = 7^2 \times 4^2
   \]

3. Using the property of exponents \( a^m \times b^m = (a \times b)^m \), we can simplify:
   \[
   A = (7 \times 4)^2
   \]

4. Simplifying further:
   \[
   A = 28^2
   \]

5. Finally, evaluating \( 28^2 \):
   \[
   A = 784
   \]

So, the area of the rectangle can be expressed in three equivalent ways:
- \( 7^2 \times 4^2 \)
- \( (7 \times 4)^2 \)
- \( 784 \)

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions to expand your understanding:
1. What is the area of a rectangle with sides \( 6^2 \) and \( 3^2 \)?
2. How does the property of exponents help simplify multiplication in geometry problems?
3. If one side of a rectangle is doubled, how does it affect the area?
4. Can you use the distributive property to break down \( (7^2 + 4^2) \times 2 \)?
5. How do you calculate the area of a rectangle if one side is an expression, such as \( x + 3 \)?

**Tip:** Remember that knowing exponent rules can simplify calculations involving geometric shapes.

This phone is right to equivalent expressions for the area of the rectangle that has the sides of 7 to the second power and 4 to the second power.

Learn how to find equivalent expressions for the area of a rectangle with sides 7^2 and 4^2. This solution explains the properties of exponents and shows step-by-step how to simplify and calculate the area, suitable for students in Grades 6-8.

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