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Annemarie26
@Annemarie26
May 2019
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1. Décomposer a = 360 x 10 a la puissance 4 et b=250x5 a la puissance 3 en un produit de facteurs premiers
2. Calculer a^b
3. Simplifier le quotient a/b . Et puis trouver deux entiers naturels n et m tél que √ab = n√m .
4. Calculer 1/b - 1/a
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nini999
Bonsoir :
1)
a = 360 × 10⁴
a = (36 × 10) × (5 × 2)⁴
a = (6² × 5 × 2) × 5⁴ × 2⁴
a = [(3×2)² × 5 × 2) × 5⁴ × 2⁴
a = (3² × 2² × 5 × 2²) × 5⁴ × 2⁴
a = (3² × 2² × 2² × 5) × 5⁴ × 2⁴
a = (3² × 2²⁺² × 5) × 5⁴ × 2⁴
a = (3² × 2⁴ × 5) × 5⁴ × 2⁴
a = 3² × 2⁴ × 5¹ × 5⁴ × 2⁴
a = 3² × 2⁴ × 2⁴ × 5¹ × 5⁴
a = 3² × 2⁴⁺⁴ × 5¹⁺⁴
a = 3² × 2⁸ × 5⁵
b = 250 × 5¹
b = (50¹ × 5¹) × 5¹
b = (5¹ × 10¹ × 5¹) × 5¹
b = (5¹ × 2¹ × 5¹ × 5¹) × 5¹
b = 5¹ × 5¹ × 5¹ × 5¹ × 2¹
b = 5¹⁺¹⁺¹⁺¹ × 2¹
b = 5⁴ × 2¹
2)
aᵇ = (3² × 2⁸ × 5⁵)^(5⁴ × 2¹)
aᵇ = (3² × 2⁸ × 5⁵)¹²⁵⁰
aᵇ = (3²)¹²⁵⁰ × (2⁸)¹²⁵⁰ × (5⁵)¹²⁵⁰
aᵇ = 3²⁵⁰ × 2¹⁰⁰⁰⁰ × 5⁶²⁵⁰
3)
a/b = (3² × 2⁸ × 5⁵)/(5⁴ × 2¹)
a/b = 3² × 2⁸⁻¹ × 5 ⁵⁻⁴
a/b = 3² × 2⁷ × 5¹
√ab = √[(3² × 2⁸ × 5⁵)×(5⁴ × 2¹)]
√ab = √(3² × 2⁸ × 5⁵ × 5⁴ × 2¹)
√ab = √(3² × 2⁸ × 2¹ × 5⁵ × 5⁴)
√ab = √(3² × 2⁸⁺¹ × 5⁵⁺⁴)
√ab = √(3² × 2⁹ × 5⁹)
√ab = √[3² × (2²×2²×2²×2²)×2 × (5²×5²×5²×5²)×5]
√ab = 3 × (2×2×2×2) × (5×5×5×5)√(2×5)
√ab = 30000√10
C'est ton tour fais b
J’espère t'avoir t'aider
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Annemarie26
Merci beaucoup
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1)
a = 360 × 10⁴
a = (36 × 10) × (5 × 2)⁴
a = (6² × 5 × 2) × 5⁴ × 2⁴
a = [(3×2)² × 5 × 2) × 5⁴ × 2⁴
a = (3² × 2² × 5 × 2²) × 5⁴ × 2⁴
a = (3² × 2² × 2² × 5) × 5⁴ × 2⁴
a = (3² × 2²⁺² × 5) × 5⁴ × 2⁴
a = (3² × 2⁴ × 5) × 5⁴ × 2⁴
a = 3² × 2⁴ × 5¹ × 5⁴ × 2⁴
a = 3² × 2⁴ × 2⁴ × 5¹ × 5⁴
a = 3² × 2⁴⁺⁴ × 5¹⁺⁴
a = 3² × 2⁸ × 5⁵
b = 250 × 5¹
b = (50¹ × 5¹) × 5¹
b = (5¹ × 10¹ × 5¹) × 5¹
b = (5¹ × 2¹ × 5¹ × 5¹) × 5¹
b = 5¹ × 5¹ × 5¹ × 5¹ × 2¹
b = 5¹⁺¹⁺¹⁺¹ × 2¹
b = 5⁴ × 2¹
2)
aᵇ = (3² × 2⁸ × 5⁵)^(5⁴ × 2¹)
aᵇ = (3² × 2⁸ × 5⁵)¹²⁵⁰
aᵇ = (3²)¹²⁵⁰ × (2⁸)¹²⁵⁰ × (5⁵)¹²⁵⁰
aᵇ = 3²⁵⁰ × 2¹⁰⁰⁰⁰ × 5⁶²⁵⁰
3)
a/b = (3² × 2⁸ × 5⁵)/(5⁴ × 2¹)
a/b = 3² × 2⁸⁻¹ × 5 ⁵⁻⁴
a/b = 3² × 2⁷ × 5¹
√ab = √[(3² × 2⁸ × 5⁵)×(5⁴ × 2¹)]
√ab = √(3² × 2⁸ × 5⁵ × 5⁴ × 2¹)
√ab = √(3² × 2⁸ × 2¹ × 5⁵ × 5⁴)
√ab = √(3² × 2⁸⁺¹ × 5⁵⁺⁴)
√ab = √(3² × 2⁹ × 5⁹)
√ab = √[3² × (2²×2²×2²×2²)×2 × (5²×5²×5²×5²)×5]
√ab = 3 × (2×2×2×2) × (5×5×5×5)√(2×5)
√ab = 30000√10
C'est ton tour fais b
J’espère t'avoir t'aider