1. Lesson 2: Power Rules
I will understand how to expand and simplify basic and complex exponents

2. Take the power of the reciprocal
Exponent
Expanded
Simplify
𝟐 𝟑
𝟐∙𝟐∙𝟐 𝟖
𝟏 𝟐∙𝟐∙𝟐
𝟏 𝟖
𝟐 −𝟑
Negative Exponents
Take the power of the reciprocal
(flip fraction)
𝟏 𝟐 −𝟑
𝟐 𝟏 ∙ 𝟐 𝟏 ∙ 𝟐 𝟏 𝟖

3. Case 1 𝟐 𝟔 𝟐 𝟐 ∙ 𝟐 𝟒 𝒙 −𝟑 ∙ 𝒙 𝟒 𝒃 −𝟓 ∙𝒃 𝟑 𝒂 𝒎 ∙ 𝒂 𝒏 = 𝒂 𝒎+𝒏 𝒙=𝒙 𝟏
Exponent
Expanded
Simplify
𝟐∙𝟐 (𝟐∙𝟐∙𝟐∙𝟐)
𝟐 𝟔
𝟐 𝟐 ∙ 𝟐 𝟒
𝒙∙𝒙∙𝒙∙𝒙 𝒙∙𝒙∙𝒙
𝒙=𝒙 𝟏
𝒙 −𝟑 ∙ 𝒙 𝟒
𝒃∙𝒃∙𝒃 𝒃∙𝒃∙𝒃∙𝒃∙𝒃
𝟏 𝒃 𝟐 =𝒃 −𝟐
𝒃 −𝟓 ∙𝒃 𝟑
Do you notice a pattern?!
When multiplying exponents with the same variable, add the exponents
𝒂 𝒎 ∙ 𝒂 𝒏 = 𝒂 𝒎+𝒏

4. Case 2
Exponent
Expanded
Simplify
( 𝟐𝒙 𝟐 ) 𝟐
𝟐 𝟐 𝒙 𝟒
(𝟐∙𝒙 ∙𝒙)
(𝟐∙𝒙 ∙𝒙)
𝟏 𝒙∙𝒙∙𝒙
𝒙 𝟑 −𝟐
𝟏 𝒙∙𝒙∙𝒙
𝟏 𝒙 𝟔 or 𝒙 −𝟔
𝒂 𝟐 𝒃 𝟑 𝟐
𝒂∙𝒂 𝒃∙𝒃∙𝒃
𝒂∙𝒂 𝒃∙𝒃∙𝒃
𝒂 𝟒 𝒃 𝟔
Do you notice a pattern?!
𝒂 𝒎 𝒃 𝒎 𝒏 = 𝒂 𝒎∙𝒏 𝒃 𝒎∙𝒏
When taking the power of a power, multiply the exponents
( 𝒂 𝒎 ) 𝒏 = 𝒂 𝒎∙𝒏

5. 𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙 𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙 𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃 𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃
Case 3
Exponent
Expanded
Simplify
𝟒 𝟕 𝟒 𝟒
𝟒∙𝟒∙𝟒∙𝟒∙𝟒∙𝟒∙𝟒 𝟒∙𝟒∙𝟒∙𝟒
𝟒 𝟑
𝟏 𝒙 𝟐 = 𝒙 −𝟐
𝒙 𝟕 𝒙 𝟗
𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙 𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙∙𝒙
𝒃 𝟐 𝒃 𝟒 𝒃 𝟕
𝟏 𝒃 = 𝒃 −𝟏
𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃 𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃∙𝒃
Do you notice a pattern?!
𝒂 𝒏 𝒂 𝒎 = 𝒂 𝒏−𝒎
When dividing powers, subtract the exponents

6. 𝟐 𝟒 𝟐 𝟒 =
𝟐 𝟒−𝟒 =
𝟐 𝟎
=??
Exponent
Expanded
Simplify
𝟐 𝟒 𝟐 𝟒
𝟏𝟔 𝟏𝟔 =
𝟐∙𝟐∙𝟐∙𝟐 𝟐∙𝟐∙𝟐∙𝟐 𝟏
𝟐 𝟎 =𝟏
𝒙 𝟎 =𝟏

7. Exponent
Rewrite
Expand
Simplify
4 1 2 4 2 2
8 1 3
3 8
3 2∙2∙2
4∙4∙4
4 3 2
4 3 64 8
8∙8