1. No category

IES Juan García Valdemora
Departamento de Matemáticas
TEMA1. HOJA 3. EJERCICIOS DE POTENCIAS
2º ESO
1. CALCULA:
2
a) (− 3) =
o) (− 3) =
1
b) (− 3) =
p) 91 =
3
c)
d)
e)
f)
g)
h)
i)
j)
q) 50 =
(− 3)4 =
(− 5)3 =
(− 5)4 =
(− 12)2 =
(− 7 )2 =
(− 7 )3 =
(− 2 )5 =
(− 2 )6 =
(− 3)0 =
0
s) (− 9 ) =
0
t) (− 13) =
4
u) (− 2 ) =
2
3
v) (− 3) − (− 1) =
3
2
w) (1 − 2 ) − (− 5 + 1) =
2 2
31
x) [(− 2) ] − [(− 3) ] =
2
1
0
y) (− 2 ) + (− 2 ) − (− 2 ) =
2
3
0
z) (− 5) + (− 5 ) − (− 5 ) =
r)
5
k) 2 =
1
l) (− 7 ) =
m) (− 2 ) =
7
n) 51 =
2. CALCULA:
a) 3−1 =
h)
b) 2−3 =
i)
c)
j)
d)
e)
f)
g)
(− 3)−1 =
(− 5)−2 =
(− 5)−3 =
(− 12 )−2 =
(− 7 )−3 =
(− 7 )−1 =
o) 5−2 =
p) 11−2 =
q) ( −11) −2 =
2−5 =
(− 2 )−5 =
k) 3−4 =
r)
l)
s)
(− 11)−1 =
(− 13)−1 =
(− 13)−2 =
m) 13−1 =
n) 51 =
3. REDUCE A UNA ÚNICA POTENCIA:
a)
63 ⋅ 6 ⋅ 65 =
k)
(− 5)8 : (− 5)4 ⋅ (− 5) =
b)
(− 7 )9 : (− 7 )5 =
l)
(8 ) : [(− 2) ⋅ (− 4) ] =
d)
[(− 2) ] =
(− 2) : [(− 2) ⋅ (− 2)] =
e)
205 : (− 4 ) =
f)
(− 36)4 : (− 9 )4
c)
4 3
9
2
4
5
[
i)
j)
(5 ) ⋅ (5 ) =
9
9
8
8
3 2
7 4
5
4 3
12
5
7
n) 2 ⋅ 8 ⋅ 2 ⋅ 16 =
(3 ) ⋅ 27 ⋅ 9
2 3
4
=
p) 315 : 813 =
=
]
(− 5) ⋅ [20 : (− 4) ] =
(6 ) ⋅ [(− 7) ⋅ (− 7)] =
9
12
m) ( a 5 )3 : (a 7 ) 2 =
o)
g) 12 9 : (− 3) ⋅ (− 4) =
h)
5 4
q)
r)
(m
3
) ( )
2
4
⋅ m : m2 =
(− 10)20 : [(− 2)9 ⋅ 59 ]
2
=
s)
[(− 3) ⋅ (− 2) ] ⋅ (6 ) =
t)
[a
5 3
5
3
] [
2
4 2
]
2
⋅ a 4 : a15 : a13 =
IES Juan García Valdemora
Departamento de Matemáticas
u)
[(− 30)
][
TEMA1. HOJA 3. EJERCICIOS DE POTENCIAS
2º ESO
]
: 519 : (− 2) ⋅ 34 =
19
3
4
y)
v) m14 : ( m8 ⋅ m) =
(b ) : (b ⋅ b) =
a ⋅ a : [a : a ] =
5 3
4
z)
3
3
4
12
4
w) ( x 2 )3 : ( x 3 ) 2 =
(8
)
⋅ 2 2 : 162
x)
=
(− 10)3 : (− 5)3
3
4. REDUCE A UNA ÚNICA POTENCIA DE EXPONENTE NATURAL:
a)
7 3 ⋅ (7 ⋅ 7 3 ) 5 =
k)
(− 3)4 : (− 3)8 ⋅ (− 3) =
b)
(− 6)9 : (− 6)−7 =
l)
c)
[(− 5) ]
(− 3)4 : [(− 3)8 ⋅ (− 3)] =
m) 124
d)
4 −3
( ) : [(− 3) ⋅ (− 4) ] =
=
(− 12)3 : [(− 12)4 ⋅ (− 12)]
−1
=
n)
e) 155 : (− 3) =
o)
814 : (− 9 ) =
p)
5
f)
4
[
9
]
(− 5) ⋅ [35 : (− 7 ) ] =
(3 ) ⋅ [(− 5) : (− 5) ] =
6
8
g) 15 : (− 5) ⋅ (− 3) =
9
h)
i)
j)
3 2
9
(4 ) ⋅ (4 )
9 −3
12
[(− 11) ] : [(− 11) ]
4 −2
5 3
(3 ) ⋅ 27 ⋅ 9
(2 ⋅ 2) : (2 )
2 −3
−4
2
3
2 4
=
(− 20)7 : [(− 4)9 ⋅ 59 ]
−1
s)
[40
t)
=
=
[(− 2) ⋅ (− 3) ] ⋅ (6 )
−1
=
12
r)
8
5
7 4
q)
2
9
4 −2
5 3
5
=
][
=
]
3
: 209 : 24 ⋅ 24 =
(− 3)4 ⋅ (− 3)7 : [122 : (−4) 2 ] =
5. Simplifica (utilizando las propiedades de las potencias) las siguientes expresiones y después calcula:
35 ⋅ 22 ⋅ 4
a)
=
33 ⋅ 9
8 ⋅ 64 ⋅ 81 ⋅ 24 ⋅ 52
d)
=
32 ⋅ 25 ⋅ 53 ⋅ 64 ⋅ 16
g)
(7 ⋅ 8)
3
4
82 ⋅ 494 ⋅ 145
=
b)
32 ⋅ 27 ⋅ 3
=
8⋅4
e)
8 ⋅ 25 ⋅ 73 ⋅ 34
=
20 ⋅ 21 ⋅ 14 ⋅ 7
h)
3 −3 ⋅ 4 ⋅ 9 −1
=
3 − 5 ⋅ 4 −1
c)
63 ⋅ 12 4 ⋅ 36
=
27 3 ⋅ 82 ⋅ 64
f)
54 4 ⋅ 103 ⋅ 52 ⋅ 152
=
1253 ⋅ 187
i)
216 ⋅ 27 −3 ⋅ 64 −1
=
12 − 4 ⋅ 82 ⋅ 36 −1
6. Reduce a una única potencia y después calcula:
a)
b)
c)
(a ) ⋅ (a ⋅ a ) =
a : [a : a ] =
(x ) ⋅ (x ) : (x )
3 −5
4
6 3
5
2
7
d)
5 2
3 −4
2 3
e)
=
(b ⋅ b) : (b : b ) =
(a ⋅ b) : (a ⋅ b ) =
(a ) ⋅ (b ) ⋅ a =
a ⋅ (b ) ⋅ b
4
6
9
5
4
10
3 4
f)
7
3 5
2 2
7 2
4 3
−4
2