### Algebra Practice: Finding the QuotientIn 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 Problem1. **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**: \[Q = 3a^9b^2\]### SolutionTherefore:\[36a^5b^3 \div 3a^9b^2 = 12a^{-4}b\]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.

Here we have We have to find the quotient that makes it a true statement

Answered: Find the quotient that makes it a true…

Find the quotient that makes it a true statement. Show work for how you for 36a5b³ ÷ ? = 12a-4b¹

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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