8.2: Exponential Properties Involving Quotients
In this lesson, you will learn how to simplify quotients of numbers and variables.
Quotient of Powers Property: For all real numbers
When dividing expressions with the same base, keep the base and subtract the exponent in the denominator (bottom) from the exponent in the numerator (top). When we have problems with different bases, we apply the rule separately for each base. To simplify
Example 1: Simplify each of the following expressions using the quotient rule.
(a)
(b)
Solution:
(a)
(b)
Power of a Quotient Property:
The power inside the parenthesis for the numerator and the denominator multiplies with the power outside the parenthesis. The situation below shows why this property is true.
Example 2: Simplify the following expression.
Solution:
Practice Set
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both.
CK12 Basic Algebra: Exponent Properties Involving Quotients (9:22)
Evaluate the following expressions.

5652 
6763 
31034 
(2233)3
Simplify the following expressions.

a3a2 
x9x5 
x10x5 
a6a 
a5b4a3b2 
4542 
5357 
(3452)2 
(a3b4a2b)3 
x6y5x2y3 
6x2y32xy2 
(2a3b38a7b)2 
(x2)2⋅x6x4 
(16a24b5)3⋅b2a16 
6a32a2 
15x55x 
(18a1015a4)4 
25yx620y5x2 
(x6y2x4y4)3 
(6a24b4)2⋅5b3a 
(3ab)2(4a3b4)3(6a2b)4 
(2a2bc2)(6abc3)4ab2c
Mixed Review
 Evaluate
xz−z whenx=8 andz=−4 .  Graph the solution set to the system
{y<−x−2y≥−6x+3 .  Evaluate
(84) .  Make up a situation that can be solved by 4!
 Write the following as an algebraic sentence: A number cubed is 8.