Potencias resueltas 1eso (1)
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MATEMÁTICAS TIMONMATE EJERCICIOS RESUELTOS DE POTENCIAS Juan Jesús Pascual 1/2 POTENCIAS RESUELTAS 1) Potencia de potencias: a) ( 2 4 42 8 3 3 3 ⋅ = = b) ( 3 3 3( 3) 9 2 2 2 - - -⋅- = = c) ( 29 2 2 3 3( 2)( 2) 6( 2) 12 3 3 3 3 - - - -⋅- ⋅- ⋅- - = = = d) ( 0 4 40 0 3 3 3 1 ⋅ = = = e) ( 29 2 2 1 3 3( 1) ( 2)( 1) 3( 1)( 2)( 1) 6 6 1 3 3 3 3 3 - - - ⋅- ⋅- ⋅- ⋅- ⋅- ⋅- - = = = = 2) Multiplicación de potencias: a) 4 2 4 2 6 2 2 2 2 + ⋅ = = b) 2 6 12 6 9 33 3 3 3 + + ⋅ ⋅ = = c) 4 2 4( 2) 4 2 2 2 2 2 2 2 - +- - ⋅ = = = d) 4 2 4( 2) 4 2 6 6 1 2 2 2 2 2 2 - - -+- -- - ⋅ = = = = e) 1 3 2 1 3 ( 2) 132 0 2 2 2 2 2 2 1 - - -++- -+- ⋅ ⋅ = = = = f) ( ( ⋅ ⋅ + ⋅ ⋅= ⋅ = ⋅ = ⋅ = = 5 7 5 7 3 4 35 47 15 28 15 28 43 27 81 3 3 3 3 3 3 3 3 g) ( ( ⋅ ⋅ + + ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ = = 3 2 3 4 2 2 4 3 23 4 32 6 4 6 6 4 6 14 25 5 125 5 5 5 5 5 5 5 5 5 5 5 3) División de potencias: a) 3 2 32 1 5 :5 5 5 5 - = = = b) 3 3 3( 3) 33 6 11 :11 11 11 11 - -- + = = = Nota teórica: En la multiplicación de potencias con la misma base, los exponentes se suman. Nota teórica: En la división de potencias con la misma base, los exponentes se restan. Nota teórica: En una potencia de potencias, los exponentes se multiplican.
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Transcript of Potencias resueltas 1eso (1)
MATEMÁTICAS TIMONMATE
EJERCICIOS RESUELTOS DE POTENCIAS Juan Jesús Pascual
1/2
POTENCIAS RESUELTAS
1) Potencia de potencias:
a) ( )24 4 2 83 3 3⋅= =
b) ( ) 33 3 ( 3) 92 2 2−− − ⋅ −= =
c) ( )223 3 ( 2) ( 2) 6 ( 2) 123 3 3 3
−−− − ⋅ − ⋅ − ⋅ − − = = =
d) ( )04 4 0 03 3 3 1⋅= = =
e) ( )2213 3 ( 1) ( 2) ( 1) 3 ( 1) ( 2) ( 1) 6
6
13 3 3 3
3
−−− ⋅ − ⋅ − ⋅ − ⋅ − ⋅ − ⋅ − − = = = =
2) Multiplicación de potencias:
a) 4 2 4 2 62 2 2 2+⋅ = =
b) 2 6 1 2 6 93 3 3 3 3+ +⋅ ⋅ = =
c) 4 2 4 ( 2) 4 2 22 2 2 2 2− + − −⋅ = = =
d) 4 2 4 ( 2) 4 2 66
12 2 2 2 2
2− − − + − − − −⋅ = = = =
e) 1 3 2 1 3 ( 2) 1 3 2 02 2 2 2 2 2 1− − − + + − − + −⋅ ⋅ = = = =
f) ( ) ( ) ⋅ ⋅ +⋅ ⋅ = ⋅ = ⋅ = ⋅ = =5 75 7 3 4 3 5 4 7 15 28 15 28 4327 81 3 3 3 3 3 3 3 3
g) ( ) ( ) ⋅ ⋅ + +⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ = =3 23 4 2 2 4 3 2 3 4 3 2 6 4 6 6 4 6 1425 5 125 5 5 5 5 5 5 5 5 5 5 5
3) División de potencias:
a) 3 2 3 2 15 : 5 5 5 5−= = =
b) 3 3 3 ( 3) 3 3 611 :11 11 11 11− − − += = =
Nota teórica : En la multiplicación de potencias con la misma base, los exponentes se suman.
Nota teórica : En la división de potencias con la misma base, los exponentes se restan.
Nota teórica : En una potencia de potencias, los exponentes se multiplican.
Potencias. Ejercicios resueltos TIMONMATE
2/2
c) 2
2 3 13
2 12 2
2 2− −
− = = =
d) 8 3 8 3 55
17 : 7 7 7
7− − + −= = =
e) 2 3 2 ( 3) 2 3 5
5 ( 3) 5 3 83 3 3 3
2 : 2 2 2 22 2 2
2 2 2 2
− − − +− − +
− − − −= = = = = =
f) ( )5 2 4 5 ( 2) 4 5 2 4 7 4 7 ( 4) 7 4 113 : 3 : 3 3 : 3 3 : 3 3 : 3 3 3 3− − − − − + − − − − += = = = = =
g) ( ) ( ) ( ) ( ) ( )− − −− − − − − − − = = = = =
5 2 15 45 2 4 3 2 4 15 4 4 4 19 48 : 4 : 2 2 : 2 : 2 2 : 2 : 2 2 : 2 2 : 2
( )− − += =19 4 19 4 232 2 2
4) Otros ejercicios de potencias:
a) ( )( )
32 2 3 66 21 15
7 3 7 21 153
5 5 5 15 5
5 5 55
⋅− −
⋅= = = = =
b) ( ) ( )3 32 3 2 3 3 3 6 9 6 9 33
13 : 3 5 : 5 3 : 3 3 3
3⋅ ⋅ − −= = = = =
c) ( )
( )
52 3 2 5 3 10 3 10 3 1313 6 7
2 3 2 6 6 63
3 3 3 3 3 3 3 33 3
3 3 3 33
⋅ +−
⋅
⋅ ⋅ ⋅= = = = = =
d) ( )
( )( )( ) ( )− − −− − − + − − − − ⋅ −
− ⋅ ⋅ − − − −
⋅= = = =
1 1 12 3 2 2 ( 3) 2 2 3 2 ( 5) ( 1) 2
1 3 2 2 ( 1) 3 4 3 ( 4)23 2
5 5 : 5 5 : 5 5 : 5 5 : 55 : 5 5 : 5 55 : 5
−− −
+= = = = = =5 2 5 2 3
3 7 43 4 7 7 4
5 : 5 5 5 15 5
5 5 5 5
e) ( ) ( )( ) ( )
3 22 3 2 ( 3) 3 2 6 6 6 ( 6) 6 6 1212 5 7
1 2 3 ( 1) 1 ( 2) 3 2 3 2 5 53 1
2 : 2 2 : 2 2 : 2 2 2 22 2
2 2 2 2 2 2 22 2
−− − − ⋅ − − ⋅ − − − +−
− − − ⋅ − − ⋅ − +− −= = = = = = =
⋅ ⋅⋅
*****
