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
