Refuerzo - Potencias - Ejercicios (II) Soluciones

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UFJVFUYB NF KL^FKL^GML] _B^FHMGL] CBIL = Nbül Ubdf`gl9 6 cgib} @b} 6 cgib}9 6 ´ 6 5+ F}mugef fh jbukl nf pubnvm~b w ml`mv`l f` zl`bu nf `l} }gdvgfh~f} pb~fhmgl} l' El}f 6 w fspbhfh~f = e' El}f +5 w fspbhfh~f > 6 =  ; 6 ´ 6 ´ 6 ; #+ 5' > ; #+5' ´ # + 5' ´ # + 5' ´ # + 5' ; m' #+ =' 5 n' Mv l~ub l` mveb #+ =' ´ #+ =' ; > = ; > ´ > ´ > ; =+ l' ²Mvì ` f} f` ~ ugp`f nf` ~ugp`f nf` mvln ulnb nf = 2 Mvlnulnb nf =9 = 5  ^ugp`f nf` mvlnulnb nf =9 = ´ = 5 ^ugp`f nf` ~ugp`f nf` mvlnulnb nf ~uf}9 = ´ #= ´ = 5 ' ; = >  ; e' ²W f ` mvln ulnb nf` ~u gp`f n f` ~ugp `f nf ~uf}2 ^ugp`f nf =9 = ´ = ; = 5 ^ugp`f nf` ~ugp`f nf ~uf}9 = ´ = 5 ; = = Mvlnulnb nf` ~ugp`f nf` ~ugp`f nf ~uf} Q#=' = [ 5 ; = :  ; >+ Mbkp`f~l `l }gdvgfh~f ~le`l9 6+ F}mugef mlnl hùkfub mbkb vhl pb~fhmgl 7 ; = ´ = ; + 3 ; #+5' ´ #+5' ´ #+5' ; 56 ; 6 ´ 6 ; + :> ; + 5 ´ 5 ´ 5 ´ 5 ´ 5 ´5 ; :+ ²Mvìh~b} ìueb`f} clw fh vh eb}|vf |vf ~gfhf <>5 jg`l} nf <>5 ìueb`f} mlnl vhl2 <>5 ´ <>5 ; <>5 5 4+ F}mugef mlnl pubnvm~b fh jbukl nf pb~fhmgl w cl``l f` zl`bu nf9 l' 56 ´ #+ 6' m' 7 ´ #+=' 5 56 ´ #+ 6' ; #+ 6' 5 ´ #+ 6' ; #+6' = ; 7 ´ #+=' 5 ; #+ =' 5 ´ #+ =' 5 ; #+ =' > ; e' + 3 ´ > n' + <??? ´ #+ <?' ´ <?? + 3 ´ > ; #+ 5' = ´ #+ 5' 5 ; #+ 5' 6 ; #+ <?' = ´  #+ <?' ´ #+ <?' 5 ; #+ <?' : ; 3+ Cl``l9 l' Q#+ 5' = ´ 6 5 [ = Q#+ 5' = ´ 6 5 [ = ; Q+ 3 ´ 56[ = ; b egfh Q#+ 5' = [ = ´ Q6 5 [ = ; e' Q#+ 5' ´ # ! 6' ´ #+ :'[ = Q#+ 5' ´ # ! 6' ´ #+ :'[ = ; b egfh m' #6 ´ l ´ e' > #6 ´ l ´ e' > ; 6 > l > e > #+5 7 ' ´ 6 : #+ 5' = ´ #6 = '  ´ #+:' = Zl`bu #+ =' ´ #+ =' ´ #+ =' ´ #+ =' 6 ´ 6 ´ 6 #+ 5' ´ #+ 5' ´ #+ 5' = 5 <+ Nbül Ubdf`gl ~vzb 6 cgib}1mlnl vhb nff``b} ~vzb ~lkegçh 6 cgib} w l }v zfy, ç}~b} clh ~fhgnb 6 cgib} mlnl vhb( ²Mvìh~b} eg}hgf~b} ~gfhf Ubdf`gl2 @b} hgf~b}9 6 ´ 6 ´ 6 ; 6 =  ; <56 eg}hgf~b} <56 _ubnvm~b 7 3< :> _b~fhmgl #+ 5' = #+ =' > 6 = + 5 : + =5 #+ >' 5 + <56 #+ >' ´ #+ >' #+5' = = + 3 457 = + = > + 5 <? : 6 5 El}f <: + > 5 3< <56 Fspbhfh~f 6 3< <: #+ 5??' = #:?' =

Transcript of Refuerzo - Potencias - Ejercicios (II) Soluciones

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UFJVFUYB NF KL^FKL^GML]

_B^FHMGL] CBIL =

Nbül Ubdf`gl9 6 cgib}

@b} 6 cgib}9 6 ´ 6

5+ F}mugef fh jbukl nf pubnvm~b w ml`mv`l f` zl`bu nf `l} }gdvgfh~f} pb~fhmgl}

l' El}f 6 w fspbhfh~f = e' El}f +5 w fspbhfh~f >

6= ; 6 ´ 6 ´ 6 ; #+ 5'

>; #+5' ´ #+ 5' ´ #+ 5' ´ #+ 5' ;

m' #+ ='5

n' Mvl~ub l` mveb

#+ =' ´ #+ =' ; >=; > ´ > ´ > ;

=+ l' ²Mvì` f} f` ~ugp`f nf` ~ugp`f nf` mvlnulnb nf =2

Mvlnulnb nf =9 =5

 

^ugp`f nf` mvlnulnb nf =9= ´ =

5

^ugp`f nf` ~ugp`f nf` mvlnulnb nf ~uf}9 = ´ #= ´ =5' ; =

> ;

e' ²W f` mvlnulnb nf` ~ugp`f nf` ~ugp`f nf ~uf}2

^ugp`f nf =9 = ́ = ; =5

^ugp`f nf` ~ugp`f nf ~uf}9 = ´ =5

; ==

Mvlnulnb nf` ~ugp`f nf` ~ugp`f nf ~uf} Q#='=[5; =

: ;

>+ Mbkp`f~l `l }gdvgfh~f ~le`l9

6+ F}mugef mlnl hùkfub mbkb vhl pb~fhmgl

7 ; = ´ = ; + 3 ; #+5' ´ #+5' ´ #+5' ; 56 ; 6 ´ 6 ;

+ :> ; + 5 ´ 5 ´ 5 ´ 5 ´ 5 ´5 ;

:+ ²Mvìh~b} ìueb`f} clw fh vh eb}|vf |vf ~gfhf <>5 jg`l} nf <>5 ìueb`f} mlnl vhl2

<>5 ´ <>5 ; <>55

4+ F}mugef mlnl pubnvm~b fh jbukl nf pb~fhmgl w cl``l f` zl`bu nf9

l' 56 ´ #+ 6' m' 7 ´ #+='5

56 ´ #+ 6' ; #+ 6'5

´ #+ 6' ; #+6'= ; 7 ´ #+='

5; #+ ='

5´ #+ ='

5; #+ ='

> ;

e' + 3 ´ > n' + <??? ´ #+ <?' ´ <??

+ 3 ´ > ; #+ 5'=´ #+ 5'

5; #+ 5'

6; #+ <?'

=´ #+ <?' ´ #+ <?'

5; #+ <?'

: ;

3+ Cl``l9

l' Q#+ 5'=´ 6

5[=

Q#+ 5'=´ 6

5[=; Q+ 3 ´ 56[

=; b egfh Q#+ 5'

=[= ´ Q6

5[=;

e' Q#+ 5' ´ # ! 6' ´ #+ :'[=

Q#+ 5' ´ # ! 6' ´ #+ :'[=; b egfh

m' #6 ´ l ´ e'>

#6 ´ l ´ e'> ;

6>l

>e

>

#+57' ´ 6

:

#+ 5'=´ #6

=' ´ #+:'

=

Zl`bu

#+ =' ´ #+ =' ´ #+ =' ´ #+ ='6 ´ 6 ´ 6

#+ 5' ´ #+ 5' ´ #+ 5'

=5

<+ Nbül Ubdf`gl ~vzb 6 cgib}1 mlnl vhb nf f``b} ~vzb ~lkegçh 6 cgib} w l }v zfy, ç}~b} clh ~fhgnb 6

cgib} mlnl vhb( ²Mvìh~b} eg}hgf~b} ~gfhf Ubdf`gl2

@b} hgf~b}9 6 ´ 6 ´ 6 ; 6=

 ; <56 eg}hgf~b}

<56

_ubnvm~b

7

3<

:>

_b~fhmgl

#+ 5'=

#+ ='

>

6=

+ 5:

+ =5

#+ >'5

+ <56

#+ >' ´ #+ >'

#+5'=

= + 3

457

=+ = >

+ 5

<?:

65

El}f

<:+ > 5

3<<56

Fspbhfh~f

6

3<

<:

#+ 5??'=

#:?'=

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UFJVFUYB NF KL^FKL^GML]

_B^FHMGL] CBIL >

<© ngzg}gýh9 > plu~f}

5¹ Ngzg}gýh9 > ´ > plu~f}

=© Ngzg}gýh9 > ´ > ´ > plu~f}………………………………

:¹ Ngzg}gýh9 > ´ > ´ > ´ > ´ > ´ > ;

<?+ ]v}~g~gwf mlnl }gdhb 2 _bu f` hùkfub |vf mbuuf}pbhnl(

l' #+ >'5´ Q#+ >'

2[5

; #+ >'<?

#+ >'5´ Q#+ >'

2[5

; #+ >'5

´ #+ >'52

; #+ >'5!52

;#+ >'<?

5 ! 52 ; <? 2 ; #<? + 5'"5 ; 3"5 ;

e' #6=´ 6

2' 9 6

5; 6

:

#6=´ 6

2' 9 6

5; 6

= ! 2 9 6

5 ; 6

= ! 2 + 5; 6

:= ! 2 + 5 ; : 2 ; : + = ! 5 ;

m' Q#+='>

[5

9 #+ ='2

; #+ ='5

Q#+='>[59 #+ ='

2; #+ ='

>´59 #+ ='

2; #+='

39 #+='

2; #+ ='

3 + 2;

 #+ ='

53 + 2 ; 5 2 ; 3 + 5 ;

n' 52

´ #5='=; 5

<3

52

´ #5='=; 5

2´ 5

= ´ = ; 5

2 ! 7 ; 5

<32 ! 7 ; <3 ;

<=+ Mbkp`f~l

l' #+ ='=

´ 7 ´ …… ; #+ =':

#+ ='=

´ 7 ´ …… ; #+ ='=´ =

5 ´ …(( ; #+ ='

:

#+ ='=´ #+='

5´ …( ; #+ ='

= ! 5 ´ #+ =' ; #+ ='

= ! 5 ! <; #+ ='

:

e' #4='59 …(( ; 4

#4='59 …(( ; 4

= ´ 5 9 … ; 4

: 9 ; 4

: + 6; 4

m' Q#+ 5'5

[=

´ # + 5' ; …((

Q#+ 5'5

[=

´ # + 5' ; #+ 5'5 ´ = 

´ #+ 5' ; #+ 5': ´ #+ 5' ; #+ 5'

: ! <;

n' 56>9 #6

=´ …(' ; 6

=

56>9 #6

=´ …(' ; #6

5'>

9 #6= ´

…(' ; 63 9 #6

=´ 6

2' ; 6

3 + = + 2; 6

= 3 + = + 2 ; = 2 ; 3+ =+ = ; 5

56>9 #6

=´ ' ; 6

=

<> + Ml`mv`l f` zl`bu nf `l} `f~ul} fh mlnl vhl nf `l} gdvl`nlnf} }gdvgfh~f}

l' #s + 6'5

; :>

#s + 6'5

; :> ; 35

#s + 6'5; 3

5s + 6 ; 3 s ; 3 ! 6 ;

e' #= ´ s + :'5

; 3<

#= ´ s + :'5

; 3< #= ´ s + :'5

; 75

=s + : ; 7 s ; #7 ! :' 9 = ;

m' #3 + s'5

; =:

#3 + s'5

; =: #3 + s'5

; :5

3 + s ; : S ; 3 + : ;

6

5

>:

7+ ]f ngzgnf vh }fdkfh~b ufm~g`ëhfb fh > plu~f} gdvl`f}, `vfdb mlnl plu~f fh b~ul} > l}ë

}vmf}gzlkfh~f cl}~l : zfmf}( ²Fh mvìh~l} plu~f} }f cl ngzgngb f` }fdkfh~b2

65

6

#+5'4

<=

7

>

:

46