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