potencias 2º
TRANSCRIPT
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POTENCIAS
2º ESO
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Definición de potencia: es el producto de a por sí misma b veces. Se lee “a elevado a b”.
es el producto de 2 por sí mismo 5 veces:
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C ASOS PARTICULARES :𝑎1=¿𝑎𝑎0=¿100=¿𝑛𝑜𝑒𝑥𝑖𝑠𝑡𝑒 01=¿010=¿1
0𝑎=¿0
![Page 4: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/4.jpg)
¿Qué pasa si la base es negativa?Miraremos si el exponente es:• PAR:
• IMPAR:
El resultado será POSITIVO
El resultado será NEGATIVO(−2 )2=+4
(−2 )3=−8
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¡MUCHA ATENCIÓN! ¿Qué diferencia hay?
(−3 )2
−32
La base es negativa (-3) y el exponente es par, el resultado será positivo
La base es positiva 3 y el exponente nos da igual cómo sea, el – se copia
¿9
¿−9
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EJEMPLOS:
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25=¿
(−2)5=¿
34=¿(−1)6=¿
(−1)37=¿
(−3)4=¿
15=¿(−1)5=¿
(−2)2=¿
(−5)0=¿
32−32
811−1
811
−141
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−24=¿
(−1)3=¿
−34=¿(−1)7=¿
(−1)2=¿
(−3)3=¿
10=¿(−1)1=¿
(−2)3=¿
(−5)0=¿
−16−1−81−11
−271
−1−81
![Page 9: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/9.jpg)
= 32= 1 3
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Potencias con exponente negativo
𝑎−𝑛= 1𝑎𝑛
1𝑎−𝑛
=𝑎+𝑛
![Page 12: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/12.jpg)
− 1272− 4=¿ 116
−1− 4=¿−1(−1)− 4=¿1
−3−1=¿−13
−3−3=¿
(−3 )−3=¿1
(−3 )3=¿
¿1−27
![Page 13: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/13.jpg)
1.Expresa estas potencias como potencias de exponente positivo:
3−4=¿
108
1210
9−5=¿
134
110−8
=¿
112−10
=¿
195
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2. Halla el valor de las siguientes potencias:
2− 4=¿
(−12 )−10
=¿
124
=116
( 2−1 )10
=210=1024
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3−5=¿
(−2 )−6=¿
135
=1243
( 1−2 )6
=1
(−2 )6=164
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PROPIEDADES DE LAS POTENCIAS
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PRODUCTO DE POTENCIAS DE LA MISMA BASE
𝑎𝑛 ·𝑎𝑚=𝑎𝑛+𝑚
DIVISIÓN DE POTENCIAS DE LA MISMA BASE
𝑎𝑛 :𝑎𝑚=𝑎𝑛−𝑚
POTENCIA DE UNA POTENCIA
(𝑎𝑛 )𝑚=𝑎𝑛 ·𝑚
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PRODUCTO DE POTENCIAS CON EL MISMO EXPONENTE:
𝑎𝑛 ·𝑏𝑛= (𝑎 ·𝑏)𝑛
DIVISIÓN DE POTENCIAS CON EL MISMO EXPONENTE:
𝑎𝑛 :𝑏𝑛=(𝑎 :𝑏)𝑛
![Page 19: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/19.jpg)
3. Reduce a una sola potencia los siguientes productos:
4− 2 ·47 ·45=¿
( 23 )3
· ( 23 )− 4
=¿
410
( 23 )−1
=¿32
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5− 10 ·57 ·56=¿
(−3 )8 · (−3 )−10 · (−3 )6=¿
53
(−3 )4=¿34
![Page 21: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/21.jpg)
4. Reduce a una sola potencia los siguientes cocientes:127 :125=¿(−7 )−20 : (−7 )4=¿
122
(−7 )−24
46 : 4−9=¿ 46 −(− 9)=¿ 415
5− 8:5−10=¿5− 8−(− 10)=¿52
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5. Reduce a una sola potencia las siguientes expresiones:[ (4− 3 )−2 ]−5=¿4− 30=¿
1430
[ (32 )−1 ]− 4=¿38
[ (10− 4 )− 3 ]2=¿1024
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REDUCE A UNA ÚNICA POTENCIA:63 ·6 ·65=¿(−7 )9 : (−7 )5=¿
[ (−2 )4 ]3=¿
(−2 )9: [ (−2 )4 · (−2 ) ]2=¿
69
(−7 )4=¿
(−2 )12=¿74
212
(−2 )9: [ (−2 )5 ]2=¿ (−2 )−1=¿−
12
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205: (−4 )5=¿
129 : [ (−3 )9 · (−4 )9 ]=¿
[20 : (−4 ) ]5=¿
(−5 )5=¿−55=¿−3125
129 :129=¿
120=¿1
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(−5 )9 · [208 : (−4 )8 ]=¿
(63 )2· [ (−7 )5 · (−7 ) ]=¿
(57 )4 · (54 )3=¿
(−5 )9 · (−5 )8=¿(−5 )17
66 · (−7 )6=¿(−42 )6=¿426
528+12=¿540
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:
(85 )4 : [ (−2 )12 · (−4 )12 ]=¿
(𝑎5 )3: (𝑎7 )2=¿
(−5 )4 · (−5 )=¿
(−5 )5=¿
820 : 812=¿88
𝑎15 :𝑎14=¿𝑎1=¿𝑎
−55=¿−3125
![Page 27: Potencias 2º](https://reader035.vdocuments.pub/reader035/viewer/2022081515/58ab94d21a28abe3188b5723/html5/thumbnails/27.jpg)
25 ·8 ·27 ·16=¿
(32 )3 ·27 ·94=¿
25 ·23 ·27 ·24=¿219
36 ·33 · (32 )4=¿
36 ·33 ·38=¿317
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315 :813=¿
(𝑚3 ·𝑚)2: (𝑚2 )4=¿
(−10 )20 : [ (−2 )9 ·59 ]2=¿
315 : (34 )3=¿315 :312=¿33=¿27
(𝑚4 )2:𝑚8=¿𝑚8 :𝑚8=¿𝑚0=¿1
1020 : [ (−10 )9 ]2=¿1020 : (−10 )18=¿
1020 :1018=¿102=¿100
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[ (−3 )5 · (−2 )5 ]3 · (64 )2=¿
[𝑎3 ·𝑎4 ]2: [𝑎15 :𝑎13 ]2=¿
(65 )3 ·68=¿ 615 ·68=¿623
(𝑎7 )2: (𝑎2 )2=¿𝑎14 :𝑎4=¿ 𝑎10