Download 7-2 Study Guide and Intervention Division Properties of Exponents

NAME ____________________________________________ DATE ____________________________ PERIOD _____________
7-2 Study Guide and Intervention
Division Properties of Exponents
Divide Monomials To divide two powers with the same base, subtract the exponents.
!!
= 𝑎 ! ! ! .
Quotient of Powers
For all integers m and n and any nonzero number a,
Power of a Quotient
For any integer m and any real numbers a and b, b ≠ 0,
Example1: Simplify
𝒂𝟒 𝒃𝟕
𝒂𝒃𝟐
. Assume that no
Example 2: Simplify
denominator equals zero.
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!! !
=
!!
!!
!
!!
= (𝑎
! ! !
)( 𝑏
3 5
=ab
𝟐𝒂𝟑 𝒃𝟓
𝟑𝒃𝟐
! !
!
=
!!
!!
.
𝟑
. Assume that no
denominator equals zero.
!! ! ! !
Group powers with the same base.
! ! !
!!
!! !
) Quotient of Powers
!
=
!
!! ! ! !
!
=
Simplify.
The quotient is 𝑎 ! 𝑏 !
=
=
Power of a Quotient
!! ! !
!! (! !) (! !)
(!)! (!
!
!) !
!! ! ! !"
Power of a Power
!"! !
!! ! ! !
Quotient of Powers
!"
The quotient is
Power of a Product
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!"
.
Exercises
Simplify each expression. Assume that no denominator equals zero.
1.
4.
7.
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!!
!!
!
!! !
!!!
Chapter 7
2.
5.
8.
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3.
!!
!!!!
6.
!!!!
!! ! !
!
!
11
9.
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!! !
!!!!
!"!!
!!! ! !
!
!!! ! !
Glencoe Algebra 1
NAME ____________________________________________ DATE ____________________________ PERIOD _____________
7-2 Study Guide and Intervention (continued)
Division Properties of Exponents
Negative Exponents Any nonzero number raised to the zero power is 1; for example, (−0.5)! = 1. Any nonzero
number raised to a negative power is equal to the reciprocal of the number raised to the opposite power; for example,
!
6!! = ! . These definitions can be used to simplify expressions that have negative exponents..
!
Zero Exponent
For any nonzero number a, 𝑎 ! = 1.
Negative Exponent Property
For any nonzero number a and any integer n, 𝑎 !! =
!
!!
n and
!
!!!
= 𝑎! .
The simplified form of an expression containing negative exponents must contain only positive exponents.
𝟒𝒂!𝟑 𝒃𝟔
Example: Simplify 𝟏𝟔𝒂𝟐𝒃𝟔𝒄!𝟓. Assume that no denominator equals zero.
!! !! ! !
!"! ! ! ! ! !!
=
!
! !!
!!
!
!"
!!
!!
! !!
!
= (𝑎 !! ! ! )( 𝑏 ! ! ! )(𝑐 ! )
!
!
= 𝑎 !! 𝑏 ! 𝑐 !
!
=
=
!
!
!
!!
(1)𝑐 !
!!
Quotient of Powers and Negative Exponent Properties
Simplify.
Negative Exponent and Zero Exponent Properties
Simplify.
!! !
The solution is
Group powers with the same base.
!!
!! !
.
Exercises
Simplify each expression. Assume that no denominator equals zero.
1.
4.
7.
!!
!!!
! !!
! !!
!!! ! !!
!! ! ! !!
Chapter 7
2.
5.
8.
!
3. !!!
!! !!
!
6.
!! !! ! !
!!! !!
!
!!!! ℓ𝓁
12
9.
!!!
!!
!! !!
!"
!
!!
!!!"!
!!
!!!! !!
Glencoe Algebra 1