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

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

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

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

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

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

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