Bonsoir,
a. 2³ x 14² = 2³ x (2 x 7)² = 2³ x 2² x 7² = 2³⁺² x 7² = 2⁵ x 7²
b. (4/3)⁸ x (3/2²)⁹ = (2²/3¹)⁸ x (3/2²)⁹ = (2²ˣ⁸ / 3¹ˣ⁸) x (3¹ˣ⁹ / 2²ˣ⁹) = (2¹⁶ / 2¹⁸) x (3⁹/3⁸) = 2¹⁶⁻¹⁸ x 3⁹⁻⁸ = 2⁻² x 3¹
c. 35³ / 21² = (5 x 7)³ / (3 x 7)² = 3⁻² x 5³ x 7³⁻² = 3⁻² x 5³ x 7¹
d. 5a³b² / (15a²) = 5a² x ab² / (5a² x 3) = ab² / 3 = 1 / (3a⁻¹b⁻²)
e.On a 125 000 = 125 x 1000 = 5³ x 10³ = 5³ x (2 x 5)³ = 5³ x 2³ x 5³ = 2³ x 5³⁺³ = 2³ x 5⁶
D'où 1/125 000 = 2⁻³ x 5⁻⁶
f. Soit n le nombre qu'on cherche
On a 2² x 2⁻⁶ x 2ⁿ x 2 = 2²⁻⁶⁺ⁿ⁺¹ = 2ⁿ⁻³
et 1/8 = 1/(2³) = 2⁻³
On en déduit que n = 0
