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Systems of Equations
Adding and Subtracting Rational Expressions with Different Denominators
Graphing Linear Equations
Raising an Exponential Expression to a Power
Horizontal Line Test
Quadratic Equations
Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
Identifying Prime and Composite Numbers
Solving Linear Systems of Equations by Graphing
Complex Conjugates
Graphing Compound Inequalities
Simplified Form of a Square Root
Solving Quadratic Equations Using the Square Root Property
Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
Degree of a Polynomial
Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
Solving Absolute Value Equations
Solving Right Triangles
Solving Rational Inequalities with a Sign Graph
Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
Inequalities
Multiplying Rational Expressions
Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Polynomials
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Conjugates
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Formulas
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Roots
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
 
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Dividing Monomials

After studying this lesson, you will be able to:

  • Divide monomials.
  • Simplify expressions with negative exponents.

Dividing Powers with the Same Base: The base stays the same; Subtract the exponents

After subtracting the exponents, you will put the remaining exponent where the largest exponent was to begin with. For example, if you have which is a division problem, we will subtract the exponents 5 -2 which gives us 3. We will be left with x 3 . We leave this in the numerator, since the largest exponent was in the numerator to begin with.

 

Example 1

We are dividing powers with the same base (x). So, we keep the base and we subtract the exponents. We will have x to the 2 nd power and we put that in the denominator since the larger exponent was in the denominator to begin with.

The answer will be . We have to put a 1 in the numerator to hold the place. You can't leave the numerator without anything there.

 

Example 2

We are dividing powers with the same base (y). So, we keep the base and we subtract the exponents. We will have y to the 3 rd power and we put that in the numerator since the larger exponent was in the numerator to begin with.

The answer will be or y 3 . We don't have to put a 1 in the denominator.

 

Example 3

We are dividing powers with the same base (a and b). So, we keep the bases and we subtract the exponents

The answer will be a 3 b.

 

Now we're going to work with expressions that have coefficients. Remember that coefficients are the numbers in front of the variables. When dividing powers with the same base, we subtract the exponents. We also divide or reduce the coefficients.

 

Example 4

The coefficients are -6 and 18 so we either divide or reduce those. In the case, we need to reduce the coefficients. The exponents of r are 2 and 2 so we subtract those. The exponents of s are 5 and 1 so we subtract those.

This will give us an answer of s because -6 and 18 reduces to -1 and 3. When we subtract the exponents of r we find that they cancel each other out. When we subtract the exponents of s, we are left with s 4 . We put that in the numerator since the larger exponent was in the numerator to begin with.

 

Example 5

The coefficients are 14 and 10 so we either divide or reduce those. In the case, we need to reduce the coefficients. 14 and 10 will reduce to 7 and 5. The exponents of x are 2 and 4 so we subtract those. The exponents of y are 1 and 1 so we subtract those. The x 2 will go in the denominator and the y 2 will go in the numerator.

This will give us an answer of

 

 

 
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