Răspuns:
Explicație pas cu pas:
1) a) 5⁻¹ = 1/5
b) (-√3)⁻¹ = -1/√3 = -√3/3
c) (3√2)⁻³ = 1/(27·2√2) = √2/108
d) (√7)⁻² = 1/(√7)² = 1/7
e) (√3/2)⁻² = (2/√3)² = 4/3
f) (-2√3/3)⁻⁴ = 3⁴/(2⁴·√3⁴) = 81/(16·9) = 9/16
g) (2/√5)⁻³ = (√5/2)³ = 5√5/8
h) (√2)²ⁿ , n ∈ Z ; (√2)²ⁿ = 2²ⁿ⁽² = 2ⁿ
2) a) (√2)³·(√2)² = (√2)³⁺² = (√2)⁵ = 2√2
b) 5³·5⁻⁶ = 5³⁻⁶ = 5⁻³ = 1/5³ = 1/125
c) (2/3)⁹ : (2/3)⁻⁹ = (2/3)⁹· (3/2)⁻⁹ = (2/3)⁹·(2/3)⁹ = (2/3)⁹⁺⁹ = (2/3)¹⁸
d) (-√5/7)⁻⁵·(-√5/7)⁶ = (-√5/7)⁻⁵⁺⁶ = -√5/7
e) [(√5)²]⁻³ = (√5)²ˣ⁽⁻³⁾ = (√5)⁻⁶ = 1/√5⁶ = 1/5³ = 1/125
f){ [(√7/√6) ·√2)]²}⁻³ = (√7/√3)⁻⁶ = (√3)⁶/(√7)⁶ = 3³/7³ = (3/7)³
g) (2/√3)³ : (4/√3)³ = (2/√3)³·(√3/4)³ = 2³/4³ = (1/2)³ = 1/8
h) (4/6)⁹:(2/3)⁻⁸ = (2/3)¹⁸·(3/2)⁻⁸ = (2/3)¹⁸·(2/3)⁸ = (2/3)²⁶
i) (√3)⁸·3³ = 3⁴·3³ = 3⁴⁺³ = 3⁷
