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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
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Solving Quadratic Equations by Completing the Square
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Division Property of Exponents

Property — Division Property of Exponents

English To divide two exponential expressions with the same base:

Compare the exponents.

• If the greater exponent is in the numerator, write the base in the numerator.

• If the greater base is in the denominator, write the base in the denominator.

Then subtract the smaller exponent from the greater. Use the result as the new exponent.

Algebra Example

 (Here, m and n are positive integers.)

 

Example 1

a. Use the Division Property of Exponents to find

b. Use the definition of exponential notation to justify your answer.

Note:

Since 3 < 4, we use the form

Solution

a. The bases are the same, so subtract the exponents.
b. Rewrite the numerator and denominator to show the factors.
Cancel the common factors.

 

Example 2

Find: 79 ÷ 76. Leave your answer in exponential notation.

Solution

The operation is division and the bases are the same. Therefore, subtract the exponents and use 7 as the base.

Note:

Since 9 > 6, we use the form

Example 3

Find: w8 ÷ w13

Solution

The operation is division and the bases are the same. Therefore, subtract the exponents and use w as the base.

Note:

Since 8 < 13, we use the form
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