Calculs de puissances Page 1 / 2
Calculs de puissances Exercice N°1 : Réduis les expressions suivantes.
1) 23 x23 = 11) (44)1 =
2) (43)3 = 12) (104)4 =
3) 55 x52 = 13) 43 x42 =
4) 54 x5-4 = 14) (104)3 =
5) 104 .10-4 = 15) (45)3 =
6) 53 x5-1 = 16) 53 : 54 =
7) 42 : 45 = 17) (53)2 =
8) 21 : 25 = 18) 42 x4-2 =
9) (33)4 = 19) 53 x5-2 =
10) (24)3 = 20) 53 x5-3 =
Exercice N°2 : Réduis les expressions suivantes.
1) (4-2 x4-1) : (4-1 x4-1) = 11) [104 x(104)5] : (104)3 = 2) [54 x(53)3] : (52)2 = 12) [53 x(51)5] : (52)4 = 3) [102 x(103)4] : (102)3 = 13) (54 x52 x54) : (53 x55) = 4) 103 : [(10-1)2 x102] = 14) 3-2 : [(34)3 x33] = 5) [43 x(45)2] : (42)4 = 15) (31 x34 x34) : (31 x35) = 6) (4-5 x4-2) : (4-2 x4-3) = 16) (103 x104) : (104 x10-1) = 7) [34 x(31)5] : (34)3 = 17) (44 x45 x43) : (43 x43) = 8) 10-3 : [(102)5 x103] = 18) (22 x25 x22) : (24 x24) = 9) (32 x33) : (33 x3-1) = 19) [22 x(24)2] : (21)2 = 10) (42 x42 x42) : (41 x41) = 20) [34 x(32)4] : (31)4 =
Calculs de puissances Page 2 / 2
Exercice N°3 : Calculer et donner le résultat sous forme de fraction irréductible
A =
2
2 1
= B =
2
3 2
= C =
2
3 2
− = D =
3
3 2
− = E = -
3
3 2
= F = 3
3
3 -
2
- =
G =
3
3 -
2 -
= H =
( )
( )
33
3 -
2
- = I =
2
5 1
=
J = 2
2
5
1 = K = 2
5
1 = L =
2
5 1 -
=
M = -
2
5 1
= N =
( )
( )
22
5 -
1
- = O = 2
2
5 -
1 - =
Exercice N°4 : Calculer après avoir simplifié l’écriture.
A = -2 2
3 2 3
7 x 5 x 2
7 x 5 x
2 = B = 2
-2 2
5 x 2
5 x 2 x 3)
(- =
C = 2 x3 x5 5 x 2 x 3
2 3 -
-2 2 3
= D = -2 2
2 -3
2 x 5
2 x
5 =
E = 0 3
3 2 0
4 x 4
2 x 3 x
2 = F = -3 3 -1
3 2
5 x 3 x 2
5 x 3 x
2 =
G =
2 8
4 8 3
11 x 7 x 3
11 x 7 x
3
= H = -1 2
3 2
5 x 3) (- x 2
5 x 3 x 2
- =
