Exponents and Multiplication Page: Name: Class: Date: Warm-­‐up Problem Review: Exponents Exponents mean repeated MULTIPLICATION. Mean… Write this expression using exponents: 3 ∙ 3 = 3^2 with variables… 𝑦 ∙ 𝑦 ∙ 𝑦 = 𝑦^3 Combining terms Expand this expression to show all of the products: with the same base 8!
8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 =
!
8
8 ∙ 8 ∙ 8
8! Apply to a variable expression: 𝑎! 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎
=
𝑎!
𝑎∙𝑎∙𝑎
= 𝑎! To divide numbers or variables with the SAME base, SUBTRACT THE EXPONENTS. Zero as an Any number raised to the “0th” power = 1 Exponent So, −8 !
= −8 !!! = −8 ! = 1 −8 !
And with variables… 𝑑!
= 𝑑 !!! = 𝑑 ! = 1 𝑑!
Makes sense, right? When the NUMERATOR = the DENOMINATOR, it equals ONE. More resources can be found on our class website: www.elliottsttims.weebly.com/resources Exponents and Multiplication Page: Name: Class: Date: Negative Exponents Apply to a variable expression: 𝑎!
𝑎∙𝑎∙𝑎
=
𝑎! 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎
1
= ! = 𝑎!! 𝑎
NEGATIVE exponents in the numerator, mean move the number to the DENOMINATOR. !!
Practice: Simplify 1.) !! = 5^5 each expression. !!
2.) !! = b 3.)
4.)
!!
= 1 !!
!!
!!"
!
= 9!! = !! More resources can be found on our class website: www.elliottsttims.weebly.com/resources Exponents and Multiplication Page: Name: Class: Date: Warm-­‐up Problem Review: Exponents Exponents mean repeated ______________________________. Mean… Write this expression using exponents: 3 ∙ 3 = with variables… 𝑦 ∙ 𝑦 ∙ 𝑦 = Combining terms Expand this expression to show all of the products: with the same base 8!
= 8!
Apply to a variable expression: 𝑎!
= 𝑎!
To divide numbers or variables with the ______________ base, ___________________ ________ _______________. Zero as an Any number raised to the “0th” power = __________ Exponent So, −8 !
= −8 !
And with variables… 𝑑!
= 𝑑!
Makes sense, right? When the ____________________= the ____________________, it equals __________. More resources can be found on our class website: www.elliottsttims.weebly.com/resources Exponents and Multiplication Page: Name: Class: Date: Negative Exponents Apply to a variable expression: 𝑎!
= 𝑎!
__________________ exponents in the numerator, mean move the number to the __________________________. !!
Practice: Simplify 1.) !! = each expression. !!
2.) !! = 3.)
4.)
!!
= !!
!!
!!"
= More resources can be found on our class website: www.elliottsttims.weebly.com/resources