Activité 8 - Exercices de synthèse

b)
Applique les propriétés des puissances.
(– 3ab)4

= (– 3)4 . a4 . b4

= (– 3)4 . a4 . b4

= 81a4b4

5a3 . (– 2a3)

= 5 . a3 . (– 2) . a3

= 5 . (– 2) . a3 . a3

= – 10a6

– 4a . 5a

= – 4 . a . 5 . a

= – 4 . 5 . a . a

= – 20a2

(– 2a2b)5

= (– 2)5 . (a2)5 . b5

= – 32 . a10 . b5

= – 32 a10b5

x . (– 2x)

= x . (– 2) . x

= (– 2) . x . x

= – 2x2

2b3. (– 2b)

= 2 . b3. (– 2) . b

= 2 . (– 2) . b3 . b

= – 4b4

– 11x . 5x

= – 11 . x . 5 . x

= – 11 . 5 . x . x

= – 55 x2

(– a4b)3

= (– a4)3 . b3

= – a12 b3

– 2 . (– a5b2)4

= – 2 . (– a5)4. (b2)4

= – 2 . a20. b8

= – 2a20b8

x2 . (– 2x3)

= x2 . (– 2) . x3

= (– 2) . x2 . x3

= – 2x5

(– a3b2)2

= (– a3)2 . (b2)2

= a6b4

(– 2a5b2)4

= (– 2)4. (a5)4. (b2)4

= 16 . a20. b8

= 16a20b8

(– b2) . (– 3b3)

= (– b2) . (– 3) . b3

= (– 3) . (– b2) . b3

= 3b5

(– 5a2b3)2

= (– 5)2. (a2)2. (b3)2

= 25 . a4 . b6

= 25a4b6

– 2x . 4x

= – 2 . x . 4 . x

= – 2 . 4 . x . x

= – 8 x2