Exponent Rules Exponent Rules
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Exponent RulesExponent Rules
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PartsParts
When a number, variable, or expression isWhen a number, variable, or expression israised to a power, the number, variable, orraised to a power, the number, variable, or
expression is called theexpression is called the base base and the power isand the power is
called thecalled the exponentexponent..
nb
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What is an Exponent?What is an Exponent?
An exponent means that you multiply the baseAn exponent means that you multiply the base
by itself that many times. by itself that many times.
For exampleFor example
xx44 == xx ●● xx ●● xx ●● xx
22 == 22 ●● 22 ●● 22 ●● 22 ●● 22 ●● 22 = 4= 4
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The Invisible ExponentThe Invisible Exponent
When an expression does not have a visibleWhen an expression does not have a visible
exponent its exponent is understood to be !.exponent its exponent is understood to be !.
!
x x =
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Exponent Rule #1Exponent Rule #1
WhenWhen multiplyingmultiplying two expressions with thetwo expressions with the
same base yousame base you addadd their exponents.their exponents.
For exampleFor example=⋅ mn bb mnb
+
=⋅ 42 x x =+42 x x=⋅ 222 2! 22 ⋅ 2!2 += "2= #=
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Exponent Rule #1Exponent Rule #1
$ry it on your own%$ry it on your own%
=⋅ mn bb mnb +
=⋅ &".! hh
=⋅"".2 2
!'&" hh =+
"!2 "" =+
2&"""
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Exponent Rule #2Exponent Rule #2 WhenWhen dividingdividing two expressions with the sametwo expressions with the same
base you base you subtractsubtract their exponents.their exponents.
For exampleFor example=m
n
b
b mn
b −
=2
4
x x =−24 x 2 x
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Exponent Rule #2Exponent Rule #2
=m
n
bb mnb −
=2
."h
h
$ry it on your own%$ry it on your own%
="
".4
"
=−2h 4h
=−!"" =2" (
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Exponent Rule #Exponent Rule #
When raisin) aWhen raisin) a po!er to a po!erpo!er to a po!er youyoumultiplymultiply the exponentsthe exponents
For exampleFor example
mn
b *+ mn
b ⋅
=
42
*+ x 42⋅
= x #
x=22 *2+ 222 ⋅
= 42= !=
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Exponent Rule #Exponent Rule #
$ry it on your own$ry it on your own
mnb *+ mnb ⋅=
2"*+., h 2"⋅= h h=
22 *"+. 22" ⋅
= 4"= #!=
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"ote"ote
When usin) this rule the exponent can not beWhen usin) this rule the exponent can not be
brou)ht in the parenthesis brou)ht in the parenthesis i there is additioni there is addition
or subtractionor subtraction
222 *2+ + x 44 2+ x≠-ou would have to use F/0 in these cases
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Exponent Rule #$Exponent Rule #$
When a product is raised to a power, eachWhen a product is raised to a power, each piece is raised to the power piece is raised to the power
For exampleFor example
m
ab*+
mm
ba=
2
*+ xy22
y x=2*,2+ ⋅ 22 2 ⋅= 2,4 ⋅= !''=
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Exponent Rule #$Exponent Rule #$
$ry it on your own$ry it on your own
mab*+ mmba=
"*+.& hk ""k h=2*"2+.# ⋅ 22 "2 ⋅= (4 ⋅= "=
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"ote"ote
$his rule is for products only. When usin) this$his rule is for products only. When usin) this
rule the exponent can not be brou)ht in therule the exponent can not be brou)ht in the
parenthesis parenthesis i there is addition or subtractioni there is addition or subtraction
2*2+ + x 22 2+ x≠-ou would have to use F/0 in these cases
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Exponent Rule #%Exponent Rule #% When a 1uotient is raised to a power, both theWhen a 1uotient is raised to a power, both the
numerator and denominator are raised to thenumerator and denominator are raised to the power power
For exampleFor example
=
m
b
am
m
b
a
=
"
y x "
"
y x
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Exponent Rule #%Exponent Rule #%
$ry it on your own$ry it on your own
=
m
b
am
m
b
a
=
2
.(k
h2
2
k
h
=
2
2
4.!'
2
2
2
4
4
!= 4=
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&ero Exponent&ero Exponent
When anythin), except ', is raised to the eroWhen anythin), except ', is raised to the ero power it is !. power it is !.
For exampleFor example ='
a !+ if a 3 '*
='
x ! + if x 3 '*
='2 !
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&ero Exponent&ero Exponent
$ry it on your own$ry it on your own
='a ! + if a 3 '*
='.!! h ! + if h 3 '*
='
!'''.!2 !=''.!" '
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"egative Exponents"egative Exponents
/f b/f b 3 ', then3 ', then
For exampleFor example
=−nb nb!
=−2 x 2
! x
=−2" 2
"
!
(
!=
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"egative Exponents"egative Exponents
/f b/f b 3 ', then3 ', then
$ry it on your own%$ry it on your own%
=−nb nb!
=−".!4 h"
!
h=−"2.! "
2
!
#
!=
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"egative Exponents"egative Exponents
$he ne)ative exponent basically flips the part$he ne)ative exponent basically flips the partwith the ne)ative exponent to the other half ofwith the ne)ative exponent to the other half of
the fraction.the fraction.
−2
!b
=
!
2b 2b=
−2
2
x
=!
2 2 x 22 x=
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'ath 'anners'ath 'anners
For a problem to be completelyFor a problem to be completely
simplified there should not be anysimplified there should not be any
ne)ative exponentsne)ative exponents
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'ixed Practice'ixed Practice
(
"
.!
d
d (,2 −
= d 42 −
= d 4
2
d
=
,4
42.2 ee
4
#
+
= e
(
#e=
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'ixed Practice'ixed Practice
( )4." q 4⋅= q 2'q=
( )2.4 lp ,,,2 pl =
,,"2 pl =
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'ixed Practice'ixed Practice
2
42
*+
*+. xy
y x22
4#
y x y x= 242# −−= y x 2 y x=
(
2" *+.
x
x x(
2# *+
x
x=
(
!
x
x= (!−
= x & x=
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'ixed Practice'ixed Practice
2"24 *+*+.& pnmnm"'!2!##!2 pnmnm ⋅=
"'!2#!#!2 pnm ++=
"'2'"' pnm=
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'ixed Practice'ixed Practice
4
*2+
*2+.#
y x
y x
−− 4*2+ −−= y x 2*2+ y x −=
*2*+2+ y x y x −−=
F2 x= xy2− /
xy2− 0 24 y+22
44 yxyx +−=
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'ixed Practice'ixed Practice
(4
.(d a
d a(4 −−
= d a 42 −= d a
4
2
d
a=