Odpowiedź:
zadanie 1
a.) (-2)×(-2)×(-2)×(-2)×(-2) = 32-2=30-2=28-2=26-2=24-2=22
1.
a)
(- 2)⁵ = - 32
(- 2)⁻⁵ = (- 1/2)⁵ = - 1/32
2⁻⁵ = (1/2)⁵ = 1/32
b)
(1/3)⁻² = 3² = 9
(- 1/3)⁻³ = (- 3)³ = - 27
(- 1/3)⁻⁴ = (-3)⁴ = 81
c)
(√3)⁴ = (√3)² * (√3)²= 3 * 3 = 9
(√3)⁻² = (1/√3)² = 1²/(√3)² = 1/3
(√3)⁻⁶ = (1/√3)⁶ = (1/√3)² * (1/√3)² * (1/√3)² = 1/3 * 1/3 * 1/3 = 1/27
d)
(√2)⁶ = (√2)² * (√2)² * (√2)² = 2 * 2 * 2 = 8
(√2)⁷ = (√2)² * (√2)² * (√2)² * √2 = 2 * 2 * 2 * √2 = 8√2
(√2)⁻⁸ = (1/√2)⁸ = (1/√2)² * (1/√2)² * (1/√2)² * (1/√2)² = 1/2 * 1/2 * 1/2 * 1/2 =
= 1/16
zad 2
2³ * 4⁶ = 2³ * (2²)⁶ = 2³ * 2¹² = 2³⁺¹² = 2¹⁵
4⁻⁵ * 8² = (2²)⁻⁵ * (2³)²=2⁻¹⁰ * 2⁶ = 2⁻¹⁰⁺⁶ = 2⁻⁴
64² : 32⁻³ = (2⁶)² : (2⁵)⁻³ = 2¹² : 2⁻¹⁵ = 2¹²⁻⁽⁻¹⁵⁾ = 2¹²⁺¹⁵ = 2²⁷
(16⁻² : 4⁻⁸) * 8⁴ = [(2⁴)⁻² : (2²)⁻⁸] * (2³)⁴ = (2⁻⁸ : 2⁻¹⁶) * 2¹² = 2⁻⁸⁺¹⁶/2¹² =
= 2⁸/2¹² = 2⁸⁻¹² = 2⁻⁴
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Odpowiedź:
zadanie 1
a.) (-2)×(-2)×(-2)×(-2)×(-2) = 32-2=30-2=28-2=26-2=24-2=22
Odpowiedź:
1.
a)
(- 2)⁵ = - 32
(- 2)⁻⁵ = (- 1/2)⁵ = - 1/32
2⁻⁵ = (1/2)⁵ = 1/32
b)
(1/3)⁻² = 3² = 9
(- 1/3)⁻³ = (- 3)³ = - 27
(- 1/3)⁻⁴ = (-3)⁴ = 81
c)
(√3)⁴ = (√3)² * (√3)²= 3 * 3 = 9
(√3)⁻² = (1/√3)² = 1²/(√3)² = 1/3
(√3)⁻⁶ = (1/√3)⁶ = (1/√3)² * (1/√3)² * (1/√3)² = 1/3 * 1/3 * 1/3 = 1/27
d)
(√2)⁶ = (√2)² * (√2)² * (√2)² = 2 * 2 * 2 = 8
(√2)⁷ = (√2)² * (√2)² * (√2)² * √2 = 2 * 2 * 2 * √2 = 8√2
(√2)⁻⁸ = (1/√2)⁸ = (1/√2)² * (1/√2)² * (1/√2)² * (1/√2)² = 1/2 * 1/2 * 1/2 * 1/2 =
= 1/16
zad 2
a)
2³ * 4⁶ = 2³ * (2²)⁶ = 2³ * 2¹² = 2³⁺¹² = 2¹⁵
b)
4⁻⁵ * 8² = (2²)⁻⁵ * (2³)²=2⁻¹⁰ * 2⁶ = 2⁻¹⁰⁺⁶ = 2⁻⁴
c)
64² : 32⁻³ = (2⁶)² : (2⁵)⁻³ = 2¹² : 2⁻¹⁵ = 2¹²⁻⁽⁻¹⁵⁾ = 2¹²⁺¹⁵ = 2²⁷
d)
(16⁻² : 4⁻⁸) * 8⁴ = [(2⁴)⁻² : (2²)⁻⁸] * (2³)⁴ = (2⁻⁸ : 2⁻¹⁶) * 2¹² = 2⁻⁸⁺¹⁶/2¹² =
= 2⁸/2¹² = 2⁸⁻¹² = 2⁻⁴