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,...
Related questions
Question
![### Algebra Practice: Finding the Quotient
In this exercise, you are asked to find the quotient that makes the equation a true statement. The problem is presented as follows:
#### Problem Statement
**Find the quotient that makes it a true statement. Show work for how you found the answer.**
\[36a^5b^3 \div ? = 12a^{-4}b^1\]
### Steps to Solve the Problem
1. **Rewrite the given equation incorporating the unknown quotient**:
\[36a^5b^3 \div Q = 12a^{-4}b\]
2. **Express the division in terms of Q**:
\[Q = \frac{36a^5b^3}{12a^{-4}b}\]
3. **Simplify the numerical coefficient**:
\[\frac{36}{12} = 3\]
4. **Apply the laws of exponents to simplify the variables**:
\[\frac{a^5}{a^{-4}} = a^{5 - (-4)} = a^{5 + 4} = a^9\]
\[\frac{b^3}{b} = b^{3 - 1} = b^2\]
5. **Combine the simplified terms**:
\[Q = 3a^9b^2\]
### Solution
Therefore:
\[36a^5b^3 \div 3a^9b^2 = 12a^{-4}b\]
So, the quotient \( Q \) is:
\[Q = 3a^9b^2\]
These steps show how to solve for the quotient that validates the given statement. Understanding how to manage and manipulate algebraic expressions and exponents is crucial in solving these types of problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c5ae3a2-e137-4f19-a2f9-517c9eb84a5f%2Fc5f9167c-615d-4b60-ae72-02cd18c6f149%2Fz6bgoiy.jpeg&w=3840&q=75)
Transcribed Image Text:### Algebra Practice: Finding the Quotient
In this exercise, you are asked to find the quotient that makes the equation a true statement. The problem is presented as follows:
#### Problem Statement
**Find the quotient that makes it a true statement. Show work for how you found the answer.**
\[36a^5b^3 \div ? = 12a^{-4}b^1\]
### Steps to Solve the Problem
1. **Rewrite the given equation incorporating the unknown quotient**:
\[36a^5b^3 \div Q = 12a^{-4}b\]
2. **Express the division in terms of Q**:
\[Q = \frac{36a^5b^3}{12a^{-4}b}\]
3. **Simplify the numerical coefficient**:
\[\frac{36}{12} = 3\]
4. **Apply the laws of exponents to simplify the variables**:
\[\frac{a^5}{a^{-4}} = a^{5 - (-4)} = a^{5 + 4} = a^9\]
\[\frac{b^3}{b} = b^{3 - 1} = b^2\]
5. **Combine the simplified terms**:
\[Q = 3a^9b^2\]
### Solution
Therefore:
\[36a^5b^3 \div 3a^9b^2 = 12a^{-4}b\]
So, the quotient \( Q \) is:
\[Q = 3a^9b^2\]
These steps show how to solve for the quotient that validates the given statement. Understanding how to manage and manipulate algebraic expressions and exponents is crucial in solving these types of problems.
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