A2 - Les puissances (exercices)
www.famillefutee.com
LES PUISSANCES
Exercice 1
Ecrire le résultat sous la forme où a est un nombre relatif et n est un entier relatif.
= 4× 4 = 8× 8
8 = (4 )× 4 = (−2)× 2
= 1 5
× 1 5
× 1 5 = 4,2× ((4,2))
= 38"× 38"
38"× 38"#
Exercice 2
Factoriser chaque expression = 4− 4%
= 5+ 5#
= (−2)− (−2) = 6− 6²
= 3%− 3+ 3 = 11 − 11
Exercice 3
Factoriser chaque expression = 17 × 10× 1354 × 10 =740 × 10² + 120 × 10
8 × 10 =27 × 10− 54 × 10
18 × 10
Exercice 4
Ecrire les expressions sous la forme × +, = 144 × 27
= 2× 5× 8 =125 × 3
27 × 5
= (3) × 9 × 5 25 × (3)× 27
A2 - Les puissances (exercices)
www.famillefutee.com
CORRECTION
Exercice 1
= 4× 4 = 4 = 4 = 8× 8
8= 8× 8 .= 8× 8 = 8. = 8 = (4 )× 4 = 4 ×× 4 = 4
= (−2)× 2= 2× 2= 2 = 2 = 1
5
× 1 5
× 1
5 = 1 5
. = 1 5
= 4,2× ((4,2)) = 4,2× 4,2×= 4,2× 4,2 = 4,2= 4,2
= 38"× 38"
38"× 38"#
= 38"
38"× 38" = 38"
38"= 3 8
.= 3 8
Exercice 2
= 4− 4% =4%× 4− 4% = 4% (4− 1) = 4%× 3 = 5+ 5# = 5#× 5+ 5# = 5# (5 + 1) = 5#× 6
= (−2)− (−2) = (−2)× (−2) − (−2)= (−2) ((−2)− 1) = (−2)× (−3) = 6− 6 = 6− 6× 6 = 6 (1 − 6) = 6× (−5)
= 3%− 3+ 3 = 3× 3 − 3× 3+ 3 = 3 (3 − 3+ 1) = 3 (9 − 3 + 1)
= 3× 7
= 11 − 11 = 11 × 11− 11 = 11 (11− 1) = 11 × 10
A2 - Les puissances (exercices)
www.famillefutee.com
Exercice 3
= 17 × 10× 1354 × 10 = 17 × 10× 10 + 1354 ×× 10 = 10 (17 × 10 + 1354)
= 10 (1700 + 1354) = 10× 3054
=740 × 10 + 120 × 10
8 × 10 = 740 × 10 + 120 × 10 × 10
8 × 10 × 10 = 10 (740 + 120 × 10 ) 8 × 10 × 10
= 740 + 120 × 10
8 × 10 = 12 740
8 × 10= 3185
2 × 10= 1592,5 × 10
=27 × 10− 54 × 10
18 × 10 = 27 × 10 − 54 × 10× 10
18 × 10× 10 = 10 (27 − 54 × 10) 10 (18 × 10)
= (27 − 54 × 10)
18 × 10 =27 − 27 × 2 × 10
18 × 10 = 27 (1 − 2 × 10)
18 × 10 = 3 × 19
2 × 10= 28,5 × 10
Exercice 4
= 144 × 27 = 12² × 3
= 2× 5× 8 = 2× 5× 2 = 2.× 5 = 2%× 5 =125 × 3
27 × 5 = 5× 3
3 × 5 = 5× 3× 3× 5 = 5.× 3 = 5 × 3 = (3) × 9 × 5
25 × (3)× 27 = 3 × 3 × 5
5 × (3)× (3) = 3 × 3 × 5 5 × 3× 3
= 3 . ..× 5 = 3× 5
