Réponse :
Explications étape par étape
Bonsoir
P = 3^3 x 5^3 x 11^3
A ................| B | 3^2 x 11
3^2 x 11^2 | C | D
5^2 x 11.....| E. | F
A x 3^2 x 11^2 x 5^2 x 11 = P
A x 3^2 x 5^2 x 11^3 = 3^3 x 5^3 x 11^3
A = (3^3 x 5^3 x 11^3)/(3^2 x 5^2 x 11^3)
A = 3^(3-2) x 5^(3-2) x 11^(3-3)
A = 3^1 x 5^1 x 11^0
A = 3 x 5
3 x 5 x B x 3^2 x 11 = 3^3 x 5^3 x 11^3
B = (3^3 x 5^3 x 11^3)/(3 x 5 x 3^2 x 11)
B = 3^(3-3) x 5^(3-1) x 11^(3-1)
B = 3^0 x 5^2 x 11^2
B = 5^2 x 11^2
5^2 x 11 x C x 3^2 x 11 = 3^3 x 5^3 x 11^3
C = (3^3 x 5^3 x 11^3)/(3^2 x 5^2 x 11^2)
C = 3^(3-2) x 5^(3-2) x 11^(3-2)
C = 3^1 x 5^1 x 11^1
C = 3 x 5 x 11
5^2 x 11^2 x 3 x 5 x 11 x E = 3^3 x 5^3 x 11^3
E = (3^3 x 5^3 x 11^3)/(3 x 5^3 x 11^3)
E = 3^(3-1) x 5^(3-3) x 11^(3-3)
E = 3^2 x 5^0 x 11^0
E = 3^2
3^2 x 11^2 x 3 x 5 x 11 x D = 3^3 x 5^3 x 11^3
D = (3^3 x 5^3 x 11^3)/(3^3 x 5 x 11^3)
D = 3^(3-3) x 5^(3-1) x 11^(3-3)
D = 3^0 x 5^2 x 11^0
D = 5^2
5^2 x 11 x 3^2 x F = 3^3 x 5^3 x 11^3
F = (3^3 x 5^3 x 11^3)/(3^2 x 5^2 x 11)
F = 3^(3-2) x 5^(3-2) x 11^(3-1)
F = 3^1 x 5^1 x 11^2
F = 3 x 5 x 11^2
3 x 5 .........| 5^2 x 11^2 | 3^2 x 11
3^2 x 11^2 | 3 x 5 x 11.. | 5^2
5^2 x 11.....| 3^2............ | 3 x 5 x 11^2
