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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Question
![**Title:** Evaluating Expressions: Identifying Mistakes
**Instructions:** Claire tried to evaluate an expression step by step. Identify Claire's mistake.
**Given Expression:**
\[ \frac{4000}{4 \cdot 10^{-5}} \]
**Steps:**
**Step 1:**
\[ \frac{4 \cdot 10^2}{4 \cdot 10^{-5}} \]
**Step 2:**
\[ = \frac{4}{4} \cdot \frac{10^2}{10^{-5}} \]
**Step 3:**
\[ = 1 \cdot 10^{2 - (-5)} \]
\[ = 1 \cdot 10^{7} \]
\[ = 10^7 \]
### Analysis:
To identify Claire's mistake, follow through her steps:
1. The original expression is \(\frac{4000}{4 \cdot 10^{-5}}\).
2. In Step 1, Claire simplifies \(4000\) as \(4 \cdot 10^2\), and the denominator remains \(4 \cdot 10^{-5}\).
3. In Step 2, she splits the fractions into separate fractions: \(\frac{4}{4} \cdot \frac{10^2}{10^{-5}}\).
- This step is correct.
4. In Step 3, Claire applies the property of exponents \( \frac{10^2}{10^{-5}} = 10^{2 - (-5)} \).
- This is correct, simplifying to \(10^{2+5} = 10^7\).
Both the steps and the final evaluated expression are correct:
\[ 10^7 = 10000000 \]
Therefore, no arithmetic or logical mistake is observed in Claire's steps. Everything appears to be correctly evaluated according to the rules of exponents and simplifying fractions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cdb4ceb-5725-4e11-93d9-ff0a52d1e35d%2Fc0c5849e-3dc1-4abe-be19-87c71688570a%2F07rm8or_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Evaluating Expressions: Identifying Mistakes
**Instructions:** Claire tried to evaluate an expression step by step. Identify Claire's mistake.
**Given Expression:**
\[ \frac{4000}{4 \cdot 10^{-5}} \]
**Steps:**
**Step 1:**
\[ \frac{4 \cdot 10^2}{4 \cdot 10^{-5}} \]
**Step 2:**
\[ = \frac{4}{4} \cdot \frac{10^2}{10^{-5}} \]
**Step 3:**
\[ = 1 \cdot 10^{2 - (-5)} \]
\[ = 1 \cdot 10^{7} \]
\[ = 10^7 \]
### Analysis:
To identify Claire's mistake, follow through her steps:
1. The original expression is \(\frac{4000}{4 \cdot 10^{-5}}\).
2. In Step 1, Claire simplifies \(4000\) as \(4 \cdot 10^2\), and the denominator remains \(4 \cdot 10^{-5}\).
3. In Step 2, she splits the fractions into separate fractions: \(\frac{4}{4} \cdot \frac{10^2}{10^{-5}}\).
- This step is correct.
4. In Step 3, Claire applies the property of exponents \( \frac{10^2}{10^{-5}} = 10^{2 - (-5)} \).
- This is correct, simplifying to \(10^{2+5} = 10^7\).
Both the steps and the final evaluated expression are correct:
\[ 10^7 = 10000000 \]
Therefore, no arithmetic or logical mistake is observed in Claire's steps. Everything appears to be correctly evaluated according to the rules of exponents and simplifying fractions.
Transcribed Image Text:On an educational website, the image can be described as follows:
---
**Exam Question:**
Select the correct step from the options listed below:
- A. Step 1
- (Circle icon for selection)
- B. Step 2
- (Circle icon for selection)
- C. Step 3
- (Circle icon for selection)
---
**Notes:**
This portion appears to be part of a multiple-choice question where students need to choose the correct step from a series of steps. Each option is accompanied by a circular selection icon, commonly used in online exams or quizzes for students to indicate their choice. There are no graphs or diagrams in this image.
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