Maureen Plants Tulips In A Rectangular Flower Bed That Is 2 3 2^3 2 3 Feet Wide And 2 4 2^4 2 4 Feet Long.What Is The Area Of The Flower Bed?A. 48 Square Feet B. 128 Square Feet C. 4,096 Square Feet D. 16,384 Square Feet

Introduction

In this problem, we are given the dimensions of a rectangular flower bed and asked to find its area. The width of the flower bed is $2^3$ feet, and the length is $2^4$ feet. To find the area, we need to multiply the width by the length. In this article, we will explore the concept of area, how to calculate it, and apply it to the given problem.

What is Area?

Area is a measure of the amount of space inside a two-dimensional shape, such as a rectangle, square, or triangle. It is calculated by multiplying the length by the width of the shape. The unit of area is typically measured in square units, such as square feet (ft²), square meters (m²), or square inches (in²).

Calculating the Area of a Rectangle

To calculate the area of a rectangle, we need to multiply the length by the width. The formula for the area of a rectangle is:

Area = Length × Width

In this case, the length of the flower bed is $2^4$ feet, and the width is $2^3$ feet. We can calculate the area by multiplying these two values:

Area = $2^4$ × $2^3$

Using Exponents to Simplify the Calculation

To simplify the calculation, we can use the rule of exponents that states:

$a^m$ × $a^n$ = $a^{m+n}$

In this case, we can rewrite the expression as:

Area = $2^{4+3}$

Using the rule of exponents, we can simplify the expression to:

Area = $2^7$

Evaluating the Expression

Now that we have simplified the expression, we can evaluate it to find the area of the flower bed. To do this, we need to calculate the value of $2^7$.

$2^7$ = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128

Therefore, the area of the flower bed is 128 square feet.

Conclusion

In this article, we explored the concept of area and how to calculate it. We applied this concept to a problem involving a rectangular flower bed with dimensions $2^3$ feet wide and $2^4$ feet long. By using the formula for the area of a rectangle and simplifying the expression using exponents, we found that the area of the flower bed is 128 square feet.

Answer

The correct answer is B. 128 square feet.

Additional Tips and Resources

• To practice calculating the area of rectangles, try using different dimensions and shapes.
• For more information on exponents and how to simplify expressions, see the resources below:

• Khan Academy: Exponents and Exponential Functions
• Mathway: Exponents and Exponential Functions
• Wolfram Alpha: Exponents and Exponential Functions

References

• Khan Academy. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.khanacademy.org/math/algebra/x2f-exponents/x2f-exponents-and-exponential-functions/x2f-exponents-and-exponential-functions/v/exponents-and-exponential-functions
• Mathway. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.mathway.com/subjects/exponents-and-exponential-functions
• Wolfram Alpha. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.wolframalpha.com/input/?i=exponents+and+exponential+functions
  Q&A: Understanding the Area of a Rectangular Flower Bed ===========================================================

Introduction

In our previous article, we explored the concept of area and how to calculate it. We applied this concept to a problem involving a rectangular flower bed with dimensions $2^3$ feet wide and $2^4$ feet long. In this article, we will answer some frequently asked questions related to the area of a rectangular flower bed.

Q: What is the formula for the area of a rectangle?

A: The formula for the area of a rectangle is:

Area = Length × Width

Q: How do I calculate the area of a rectangle with dimensions $2^3$ feet wide and $2^4$ feet long?

A: To calculate the area, you can multiply the length by the width:

Area = $2^4$ × $2^3$ = $2^{4+3}$ = $2^7$ = 128 square feet

Q: What is the unit of area?

A: The unit of area is typically measured in square units, such as square feet (ft²), square meters (m²), or square inches (in²).

Q: Can I use a calculator to calculate the area of a rectangle?

A: Yes, you can use a calculator to calculate the area of a rectangle. Simply enter the length and width of the rectangle, and the calculator will give you the area.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you can use the rule of exponents that states:

$a^m$ × $a^n$ = $a^{m+n}$

For example, if you have the expression $2^4$ × $2^3$, you can simplify it by adding the exponents:

$2^4$ × $2^3$ = $2^{4+3}$ = $2^7$

Q: What if I have a rectangle with dimensions that are not powers of 2?

A: If you have a rectangle with dimensions that are not powers of 2, you can still calculate the area by multiplying the length by the width. For example, if the length is 5 feet and the width is 3 feet, the area would be:

Area = 5 × 3 = 15 square feet

Q: Can I use the area formula to calculate the perimeter of a rectangle?

A: No, the area formula is used to calculate the area of a rectangle, not the perimeter. To calculate the perimeter of a rectangle, you need to use the formula:

Perimeter = 2 × (Length + Width)

Conclusion

In this article, we answered some frequently asked questions related to the area of a rectangular flower bed. We hope that this article has helped you understand the concept of area and how to calculate it.

Additional Tips and Resources

• To practice calculating the area of rectangles, try using different dimensions and shapes.
• For more information on exponents and how to simplify expressions, see the resources below:

• Khan Academy: Exponents and Exponential Functions
• Mathway: Exponents and Exponential Functions
• Wolfram Alpha: Exponents and Exponential Functions

References

• Khan Academy. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.khanacademy.org/math/algebra/x2f-exponents/x2f-exponents-and-exponential-functions/x2f-exponents-and-exponential-functions/v/exponents-and-exponential-functions
• Mathway. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.mathway.com/subjects/exponents-and-exponential-functions
• Wolfram Alpha. (n.d.). Exponents and Exponential Functions. Retrieved from https://www.wolframalpha.com/input/?i=exponents+and+exponential+functions