Exponent Review 2 Name:____________________ Investigating Dividing with Power to Power Rule 1. Write each of the following in expanded form. Then write the answer in exponential form with a single base and power. Expanded Form Exponential Form !
!
!
!
𝑎 ∙𝑎
𝑎∙𝑎∙𝑎∙𝑎∙𝑎∙𝑎
𝑎!
!
Example: !! ! ! =
𝑏 ∙𝑏
𝑏∙𝑏∙𝑏∙𝑏
𝑏!
!
𝑎!
𝑏
! !
𝑎
𝑏!
! !
𝑎
𝑏𝑥 !
2. What do you notice when you raise division to a power? 3. Finish the following equation to express what you noticed. 𝑎! !
= 𝑏!
Exponent Review 2 Name:____________________ Investigating Zero Exponent Rule 1. Write each of the following in expanded form. Then write it using your dividing same bases rule. The answer should be the same for each column. Make sure to write your final answer in simplified form. Expanded Form Using Dividing Simplified Form Same Bases Rule !!
2∙2∙2
2!
Example: !! 1 = 1 = 2!!! = 2! 2∙2∙2
2!
5!
5!
3!
3!
𝑥!
!
𝑥
𝑥 ! !
𝑦 2. What do you notice when you raise any number to the 0 power? 3. Finish the following equation to express what you noticed. 𝑎! = Exponent Review 2 Name:____________________ Investigating Negative Exponent Rule 1. Write each of the following in expanded form. Then write it using your dividing same bases rule. The answer should be the same for each column. Make sure to write your final answer in exponential form. Expanded Form Using Dividing Exponential Form Same Bases Rule (with negative & positive exponents) !
!!
2∙2
1
1
2
!!
Example: !! !!!
!!
= 2
=
=
2
=
2
2∙2∙2 2
2!
2!
5!
!
5
3!
!"
3
𝑥!
𝑥!
𝑥 !! 𝑦 !! 2. What do you notice when you raise a number to a negative exponent? 3. Finish the following equation to express what you noticed. 𝑎!! =