College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
Section: Chapter Questions
Problem 50E
Related questions
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![**Question 12: Simplification Problem**
**Task:** Simplify the expression:
\[
(5e^{-5})^{-2}
\]
**Answer:**
___________
**Explanation:**
To simplify the expression \((5e^{-5})^{-2}\), follow these steps:
1. **Apply the Power Rule:**
The power of a power rule states \((a^m)^n = a^{mn}\). Therefore, \((e^{-5})^{-2} = e^{10}\).
2. **Apply the Power to the Coefficient:**
\(5^{-2} = \frac{1}{5^2} = \frac{1}{25}\).
3. **Combine the Results:**
The expression becomes \(\frac{1}{25} \cdot e^{10}\).
Thus, the simplified expression is:
\[
\frac{e^{10}}{25}
\]
Enter the simplified result in the provided answer box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabe9e786-be4a-454e-b2cf-16d08b96c793%2Fcec12afb-5eb7-4c70-a5bd-5589fce5af99%2Fsnmeqx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 12: Simplification Problem**
**Task:** Simplify the expression:
\[
(5e^{-5})^{-2}
\]
**Answer:**
___________
**Explanation:**
To simplify the expression \((5e^{-5})^{-2}\), follow these steps:
1. **Apply the Power Rule:**
The power of a power rule states \((a^m)^n = a^{mn}\). Therefore, \((e^{-5})^{-2} = e^{10}\).
2. **Apply the Power to the Coefficient:**
\(5^{-2} = \frac{1}{5^2} = \frac{1}{25}\).
3. **Combine the Results:**
The expression becomes \(\frac{1}{25} \cdot e^{10}\).
Thus, the simplified expression is:
\[
\frac{e^{10}}{25}
\]
Enter the simplified result in the provided answer box.
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