Integer Exponents and the Quotient Rule
Example 1:
𝒙𝟏𝟎
𝒙𝟕
=
𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙
𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙
=
The Quotient Rule: When dividing terms of the same base, subtract
the exponents.
𝒙𝟏𝟎
𝒙𝟕
= 𝒙𝟏𝟎−𝟕 =
Example 2:
𝒙𝟕
𝒙𝟏𝟎
=
𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙
𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙
=
Using the Quotient Rule:
𝟕
𝒙𝟏𝟎
= 𝒙𝟕−𝟏𝟎 = 𝒙−𝟑 =
𝟏
𝒙𝟑
NOTE:
𝟐𝟒 = 𝟐 ∙ 𝟐 ∙ 𝟐 ∙ 𝟐 = 𝟏𝟔
𝟐𝟑 = 𝟐 ∙ 𝟐 ∙ 𝟐 = 𝟖
𝟐𝟐 = 𝟐 ∙ 𝟐 = 𝟒
𝟐𝟏 = 𝟐 = 𝟐
𝟐𝟎 = 𝟏
𝟐−𝟏 =
𝟐−𝟐 =
(Any base raised to the ZERO Power is 𝟏)
𝟏
𝟐
𝟏
𝟐∙𝟐
=
𝟏
𝟒
1
Example 3:
a.)
𝟑−𝟒 =
b.)
𝟔𝟎 =
c.)
(−𝟐)−𝟒 =
d.)
−𝟐−𝟒 =
e.)
f.)
𝟏
𝟐−𝟑
𝒙𝟏𝟐
𝒙𝟑
=
=
2
Integer Exponents and
the Quotient Rule
Practice Problems
Simplify each expression. Write your answers with positive exponents
only.
1.
2.
𝒙𝟏𝟒
𝒙𝟖
𝒙𝟖
𝒙𝟏𝟒
3.
𝟓𝟎
4.
(−𝟑)𝟑
5.
−𝟑𝟑
6.
(−𝟑)−𝟑
7.
−𝟑−𝟑
3