Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem Statement:**
The width of a rectangle is \(\sqrt[3]{8^2}\) ft, and the length is \(512^{\frac{2}{3}}\) ft. What is the area of the rectangle?
**Solution:**
To find the area of the rectangle, use the formula:
\[ \text{Area} = \text{Width} \times \text{Length} \]
**Step 1: Calculate the Width**
\[
\sqrt[3]{8^2} = \sqrt[3]{64} = 4 \text{ ft}
\]
**Step 2: Calculate the Length**
\[
512^{\frac{2}{3}} = (512^{\frac{1}{3}})^2 = 8^2 = 64 \text{ ft}
\]
**Step 3: Calculate the Area**
\[
\text{Area} = 4 \, \text{ft} \times 64 \, \text{ft} = 256 \, \text{ft}^2
\]
**Answer:**
The area of the rectangle is \(256 \, \text{ft}^2\).
**Diagram Explanation:**
The diagram shows a rectangle with sides labeled to represent the area in square feet (\( \text{ft}^2 \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f125004-2f09-4033-82db-f975d321372e%2F5b9d31ed-8e01-4323-9c91-2a762e427fed%2Ft2ohata_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The width of a rectangle is \(\sqrt[3]{8^2}\) ft, and the length is \(512^{\frac{2}{3}}\) ft. What is the area of the rectangle?
**Solution:**
To find the area of the rectangle, use the formula:
\[ \text{Area} = \text{Width} \times \text{Length} \]
**Step 1: Calculate the Width**
\[
\sqrt[3]{8^2} = \sqrt[3]{64} = 4 \text{ ft}
\]
**Step 2: Calculate the Length**
\[
512^{\frac{2}{3}} = (512^{\frac{1}{3}})^2 = 8^2 = 64 \text{ ft}
\]
**Step 3: Calculate the Area**
\[
\text{Area} = 4 \, \text{ft} \times 64 \, \text{ft} = 256 \, \text{ft}^2
\]
**Answer:**
The area of the rectangle is \(256 \, \text{ft}^2\).
**Diagram Explanation:**
The diagram shows a rectangle with sides labeled to represent the area in square feet (\( \text{ft}^2 \)).
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