3exponent_rules se pt 1.ppt

7/25/2019 3Exponent_Rules SE pt 1.ppt

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Exponent RulesExponent Rules



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



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



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 =



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= #=




$ry it on your own%$ry it on your own%

=⋅ mn bb mnb +

=⋅ &".! hh

=⋅"".2 2

!'&" hh =+

"!2 "" =+

2&"""



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




=m

n

bb mnb −

=2

."h

h


="

".4

"

=−2h 4h

=−!"" =2" (



Exponent Rule #Exponent Rule #

When raisin) aWhen raisin) a po!er to a po!erpo!er to a po!er youyoumultiplymultiply the exponentsthe exponents


mn

b *+ mn

b ⋅

=

42

*+ x 42⋅

= x #

x=22 *2+ 222 ⋅

= 42= !=



Exponent Rule #Exponent Rule #

$ry it on your own$ry it on your own

mnb *+ mnb ⋅=

2"*+., h 2"⋅= h h=

22 *"+. 22" ⋅

= 4"= #!=



"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



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


m

ab*+

mm

ba=

2

*+ xy22

y x=2*,2+ ⋅ 22 2 ⋅= 2,4 ⋅= !''=



Exponent Rule #$Exponent Rule #$


mab*+ mmba=

"*+.& hk ""k h=2*"2+.# ⋅ 22 "2 ⋅= (4 ⋅= "=



"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



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


=

m

b

am

m

b

a

=

"

y x "

"

y x



Exponent Rule #%Exponent Rule #%


=

m

b

am

m

b

a

=

2

.(k

h2

2

k

h

=

2

2

4.!'

2

2

2

4

4

!= 4=



&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 !



&ero Exponent&ero Exponent


='a ! + if a 3 '*

='.!! h ! + if h 3 '*

='

!'''.!2 !=''.!" '



"egative Exponents"egative Exponents

/f b/f b 3 ', then3 ', then


=−nb nb!

=−2 x 2

! x

=−2" 2

"

!

(

!=




/f b/f b 3 ', then3 ', then


=−nb nb!

=−".!4 h"

!

h=−"2.! "

2

!

#

!=




$he ne)ative exponent basically flips the part$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=



'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



'ixed Practice'ixed Practice

(

"

.!

d

d (,2 −

= d 42 −

= d 4

2

d

=

,4

42.2 ee

4

#

+

= e

(

#e=




( )4." q 4⋅= q 2'q=

( )2.4 lp ,,,2 pl =

,,"2 pl =




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=




2"24 *+*+.& pnmnm"'!2!##!2 pnmnm ⋅=

"'!2#!#!2 pnm ++=

"'2'"' pnm=




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 +−=




(4

.(d a

d a(4 −−

= d a 42 −= d a

4

2

d

a=

3exponent_rules se pt 1.ppt

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