4000 4-10-5 4- 102 4 10-5 Step 1 4 10 4 10 5 Step 2 1-10 Step 3

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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**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:**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.
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.
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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