Laws of Exponents Recap
Investigation #1: Product of Powers with the Same Base Property Expand the following expressions. Then, rewrite the expanded form using exponents. Original Product Expanded Form Single Power 1) 2 i2 2) w3 iw 4 3) p 4 i p 2
2
3
2
( )(3x ) 5) (5x y )( 2 x y ) 4) 32 x4
4
Using the statement you wrote, express the shortcut algebraically. Product of Powers with the Same Base Property: a! ∗ a! = ____________ Investigation #2: Power to a Power Property
Expand the following expressions. Then, rewrite the expanded form using exponents.
Original Product Expanded Form Single Power 4
4
( ) 2) (5 ) 3) ( w ) 1) 22
3
3
4
Using the statement you wrote, express the shortcut algebraically. Power of a Power Property for exponents (a )
m
n
= ______________ Investigation #4: Quotient of Powers Property
Use the definition of an exponent to expand the following expressions. Then rewrite the expanded form using exponents. Original Quotient Expanded Form 25
23
h8
2) 3 h
w9 h4
3) 2 3 hw
12d 15t 7
4) 10d 8t
1) Single Power Using the statement you wrote, write the shortcut algebraically. Quotient of Powers Property for Exponents am
= ______________ an
Investigation #3: Power of a Product/Quotient Property
Use the definition of an exponent to expand the following expressions. Then rewrite the expanded form using exponents. Original Product/Quotient Expanded Form Product/Quotient of Powers 4
1) ( 2x ) 3
2) ( −4a ) 5
( )
3) h3t 2
⎛ 2 ⎞
4) ⎜ ⎟ ⎝ 5 ⎠
3
! 3$
5) # 2 & "y %
Using the statement you wrote, write the shortcut algebraically. Power of a Product Property for exponents m
( ab )
= ______________ m
⎛ a ⎞
Power of a Quotient Property for exponents ⎜ ⎟ =______________ ⎝ b ⎠
Summary Of Exponent Laws
Multiplying Same Bases Power to a Power Quotient of Powers Dominoes Take a picture of your finished dominos and add below. Power of a Product/Quotient Laws of Exponents Practice
Simplify the following using exponent rules. 1. 3𝑥 ! ∙ −5𝑥 ! 3. −9𝑥 ! 𝑦 ! 4𝑥𝑦 ! 5. 𝑥 !
! 2. 4𝑥 ! ∙ 𝑥 ! 4. −15𝑥 ! 𝑦 ! 4𝑥 ! 𝑦 ! 6. 2𝑥 ! 𝑦 ! ! 7. !! ! !
8. !! !!
!
!!!
3
9. 4 x y
2x
12. 2𝑥 2𝑥 !
10. ! 11. 18 xy 6
− 6y5
− 14 x 9 y 8
− 7 x9 y 2
14. 𝑥 ! 5𝑥 ! ! !! !
13. (!! ! !)!