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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Why do you have to fill in a zero placeholder for the tabular method?
![**Problem:**
Multiply \(-9m^6n \cdot 8m^7n^5\). Explain or show how you got your answer.
**Solution:**
To solve this multiplication problem involving polynomials, we'll use the properties of exponents.
1. **Multiply the coefficients:**
\(-9 \times 8 = -72\)
2. **Apply the product of powers rule to the variables:**
- For \(m\), add the exponents:
\[m^6 \cdot m^7 = m^{6+7} = m^{13}\]
- For \(n\), add the exponents:
\[n^1 \cdot n^5 = n^{1+5} = n^{6}\]
3. **Combine the results:**
The product is \(-72m^{13}n^{6}\).
Therefore, the final answer is \(-72m^{13}n^{6}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9244975e-7244-4c17-ad08-1777c6b82fb3%2F6fc48d75-f2f3-41c4-822d-7e0af59642dc%2Fhfqe6pi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Multiply \(-9m^6n \cdot 8m^7n^5\). Explain or show how you got your answer.
**Solution:**
To solve this multiplication problem involving polynomials, we'll use the properties of exponents.
1. **Multiply the coefficients:**
\(-9 \times 8 = -72\)
2. **Apply the product of powers rule to the variables:**
- For \(m\), add the exponents:
\[m^6 \cdot m^7 = m^{6+7} = m^{13}\]
- For \(n\), add the exponents:
\[n^1 \cdot n^5 = n^{1+5} = n^{6}\]
3. **Combine the results:**
The product is \(-72m^{13}n^{6}\).
Therefore, the final answer is \(-72m^{13}n^{6}\).
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