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MATEMÁTICAS 4º ESO
EJERCICIOS RESUELTOS DE FRACCIONES, POTENCIAS Y LOGARITMOS

1. Operaciones con fracciones:

 8

24 

1
−3 − − − 50 ⋅ 1 −  −3 − −4 − 50 ⋅ 




 2 7
3
6
25 

25  −3 −[−6 ]


=
=
a)
=
= 3 : −  = −

1
7
1

 1
 2
7


−4 +
−
−4 − − 
−4 −  − 1

 2

2



2
2

 1

1 
 1 5
6
3 − − − 5 ⋅ 1 −  3 − − −  3 − − 




 2
6
12
2 
 2 2 
 2  3 + 3
b)
=
=
=
=
=−
1
7
7
7
7
7
−4 +
−
−
−
−
2
2
2
2
2

1
10 − 1
9
9
9
10= 1−
10
c) 1−
= 1− 10 = 1− 10 = 1− 10 =
1
1
1
10
9 − 10
1−
1−
1−
1−
1
10 − 1
9
9
9
1−
10
10
10
1−

9
9 1
81 10 + 81 91
= 1− 10 = 1+
: = 1+
=
=
−1
10 9
10
10
10
92 1
3
+ 3−
3 4⋅
2
3 1
1
− 2+
5 =
d) 4 2
1
5⋅
2

11 3
12 ⋅ 2
1 11
11 ⋅ 4 3 ⋅ 5
⋅
4 5 = 12 2 ⋅ 11 = 11 ⋅ 4 ⋅ 3 ⋅ 5 ⋅ 2 = 1
5
5
12 ⋅ 2 ⋅ 11 ⋅ 5
2
2

2. Operaciones conpotencias:
−2

3

a) 16−2 ⋅ 4 3 = ( 2 4 ) ⋅ ( 2 2 ) = 2−8 ⋅ 2 6 = 2−8+6 = 2−2 =
2

3

1
4

2

2
2
4 2 ⋅ 12 3 ⋅ 152 (2 ) ⋅ (2 ⋅ 3) ⋅ (3 ⋅ 5)
2 4 ⋅ 2 6 ⋅ 33 ⋅ 32 ⋅ 5 2 2 10 ⋅ 35 ⋅ 52
b)
=
==
= 2 4 ⋅ 3−4 ⋅ 5 2
3
2
3
6
6
3
6
9
2 3
3 2
3
9 ⋅8 ⋅3
3 ⋅2 ⋅3
2 ⋅3
(3 ) ⋅ (2 ) ⋅ 3
4

2

3

−3

3
2
2
8 4 ⋅ 153 ⋅ 182 ⋅ 12−3 (2 ) ⋅ (3 ⋅ 5) ⋅ (2 ⋅ 3 ) ⋅ ( 2 ⋅ 3)
c)
=3
2
20 3 ⋅ 27 2 ⋅ 3−3
(2 2 ⋅ 5) ⋅(33 ) ⋅ 3−3

Juan Pascual

1/7

=

Matemáticas 4ª ESO

Ejercicios Resueltos de Fracciones, Potencias y Logaritmos

2 12 ⋅ 3 3 ⋅ 5 3 ⋅ 2 2 ⋅ 3 4 ⋅ 2−6 ⋅3−3
2 8 ⋅ 3 4 ⋅ 53
= 6 3 3 = 2 2 ⋅ 3 = 12
2 6 ⋅ 5 3 ⋅ 36 ⋅ 3−3
2 ⋅3 ⋅5

=

−1

 23 
27 ⋅ 81 ⋅ 3 ⋅   ⋅ 2 3
 
3
 
−1

d)

3 3
⋅2
36
23
=
= 6 =1
2 2 33
3
32 ⋅ 2 2 ⋅32 ⋅ ⋅ 4 ⋅ 1
3 2

4

−1

(33 )

−2

−2
 1  4 27
36 ⋅   ⋅ ⋅ ⋅ (2 0 )

 3  3 16



⋅ 3 4 ⋅ 34 ⋅

3. Haz las siguientes operaciones con radicales:

3

a)

4 3
(33...