Introduction to Dividing Monomials
Divide MonomialsLearning Outcomes
By the end of this section, you will be able to:- Simplify expressions using the Quotient Property of Exponents
- Simplify expressions with zero exponents
- Simplify expressions using the Quotient to a Power Property
- Simplify expressions by applying several properties
- Divide monomials
readiness quiz
Before you get started, take this readiness quiz.- Simplify: [latex]\frac{8}{24}[/latex].If you missed the problem, review [link].
- Simplify: [latex]{\left(2{m}^{3}\right)}^{5}[/latex].If you missed the problem, review [link].
- Simplify: [latex]\frac{12{x}^{}}{12y}[/latex].If you missed the problem, review [link].
Divide Monomials
We have now seen all the properties of exponents. We'll use them to divide monomials. Later, you'll use them to divide polynomials. Find the quotient: [latex]56{x}^{5}\div 7{x}^{2}[/latex]. Solution[latex]56{x}^{5}\div 7{x}^{2}[/latex] | |
Rewrite as a fraction. | [latex]\frac{56{x}^{5}}{7{x}^{2}}[/latex] |
Use fraction multiplication to separate the number part from the variable part. | [latex]\frac{56}{7}\cdot \frac{{x}^{5}}{{x}^{2}}[/latex] |
Use the Quotient Property. | [latex]8{x}^{3}[/latex] |
[latex]\frac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}[/latex] | |
Use fraction multiplication. | [latex]\frac{42}{-7}\cdot \frac{{x}^{2}}{x}\cdot \frac{{y}^{3}}{{y}^{5}}[/latex] |
Simplify and use the Quotient Property. | [latex]-6\cdot x\cdot \frac{1}{{y}^{2}}[/latex] |
Multiply. | [latex]-\frac{6x}{{y}^{2}}[/latex] |
[latex]\frac{24{a}^{5}{b}^{3}}{48a{b}^{4}}[/latex] | |
Use fraction multiplication. | [latex]\frac{24}{48}\cdot \frac{{a}^{5}}{a}\cdot \frac{{b}^{3}}{{b}^{4}}[/latex] |
Simplify and use the Quotient Property. | [latex]\frac{1}{2}\cdot {a}^{4}\cdot \frac{1}{b}[/latex] |
Multiply. | [latex]\frac{{a}^{4}}{2b}[/latex] |
[latex]\frac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}[/latex] | |
Simplify and use the Quotient Property. | [latex]\frac{2{y}^{6}}{3{x}^{4}}[/latex] |
[latex]\frac{\left(3{x}^{3}{y}^{2}\right)\left(10{x}^{2}{y}^{3}\right)}{6{x}^{4}{y}^{5}}[/latex] | |
Simplify the numerator. | [latex]\frac{30{x}^{5}{y}^{5}}{6{x}^{4}{y}^{5}}[/latex] |
Simplify, using the Quotient Rule. | [latex]5x[/latex] |
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- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].