Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![**Problem Statement:**
Simplify completely. Write your answer using **positive** exponents only:
\[
(2w^5p^4v)(8w^{-8}v^{15})
\]
**Instructions:**
1. Combine the coefficients (numerical parts).
2. Apply the laws of exponents for each variable:
- \( w^{m} \cdot w^{n} = w^{m+n} \)
- \( p^{m} \cdot p^{n} = p^{m+n} \)
- \( v^{m} \cdot v^{n} = v^{m+n} \)
3. Ensure all exponents are positive in your final answer.
**Example Solution:**
- Coefficients: \(2 \times 8 = 16\)
- For \(w\): \(w^5 \times w^{-8} = w^{5+(-8)} = w^{-3}\)
- For \(p\): Since there is only \(p^4\), it remains \(p^4\).
- For \(v\): \(v \times v^{15} = v^{1+15} = v^{16}\)
Combine results:
\[ 16p^4v^{16}w^{-3} \]
Since only positive exponents are allowed, convert \(w^{-3}\) to \(\frac{1}{w^3}\):
The simplified answer is:
\[ \frac{16p^4v^{16}}{w^3} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c232805-cfb8-414c-aa30-333291dc38f1%2Fc374877b-5874-45c2-96cc-d14490b7edbb%2Fvt5rf4o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Simplify completely. Write your answer using **positive** exponents only:
\[
(2w^5p^4v)(8w^{-8}v^{15})
\]
**Instructions:**
1. Combine the coefficients (numerical parts).
2. Apply the laws of exponents for each variable:
- \( w^{m} \cdot w^{n} = w^{m+n} \)
- \( p^{m} \cdot p^{n} = p^{m+n} \)
- \( v^{m} \cdot v^{n} = v^{m+n} \)
3. Ensure all exponents are positive in your final answer.
**Example Solution:**
- Coefficients: \(2 \times 8 = 16\)
- For \(w\): \(w^5 \times w^{-8} = w^{5+(-8)} = w^{-3}\)
- For \(p\): Since there is only \(p^4\), it remains \(p^4\).
- For \(v\): \(v \times v^{15} = v^{1+15} = v^{16}\)
Combine results:
\[ 16p^4v^{16}w^{-3} \]
Since only positive exponents are allowed, convert \(w^{-3}\) to \(\frac{1}{w^3}\):
The simplified answer is:
\[ \frac{16p^4v^{16}}{w^3} \]
Expert Solution
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Given query is to simplify the expression.
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