Bonjour , pouvez vous m’aider à cette exercice 28 Merci

Bonjour

Calcul de puissance :

a^n + b^n => pas de simplification possible

a^n x b^n = (a x b)^n

a^n/a^m = a^(n-m)

a^n x a^m = a^(n+m)

Indiquer si vrai ou faux et justifier :

3^(-5) + 3^(-7) = 3^(-12)

Faux

3^(-5) + 3^(-7) = 3^(-5) x (1 + 3^(-2)) = 1/3^5 x (1 + 1/3^2) = 1/3^5 x (1 + 1/9) = 1/3^5 x (9/9 + 1/9) = 1/3^5 x 10/9 = 10/3^(5+2) = 10/3^7

Et

3^(-12) = 1/3^12

3 x 10^8 = 30^8

Faux

3 x 10^8 = 3 x 100000000 = 300000000

Et

30^8 = 30 x 30 x 30 x 30 x 30 x 30 x 30 x 30 = 6,56 x 10^11

5^(-4) x 5^10 = 5^6

Vrai

5^(-4) x 5^10 = 5^(-4+10) = 5^6

2^50 x 5^50 = 10^100

Faux

2^50 x 5^50 = (2 x 5)^50 = 10^50

12^100 x 1,5^50 x 6^(-149) = 6

Vrai

= 12^100 x 1,5^50 x 6^(-149)

= (2 x 6)^100 x (3/2)^50 x 6^(-149)

= 2^100 x 6^100 x 3^50 x 2^(-50) x 6^(-149)

= 2^(100-50) x 6^(100-149) x 3^50

= 2^50 x 6^(-49) x 3^50

= (2 x 3)^50 x 6^(-49)

= 6^50 x 6^(-49)

= 6^(50-49)

= 6