Odpowiedź:
zad 25
I. (2√3)² =4 * 3 = 12
II. 2√2 * 4√2 = 2 * 4 * √(2 * 2) = 8√4 = 8 * 2 = 16
III. 4√18/√2 =4√(18/2) = 4√9 = 4 * 3 = 12
Odp: B
zad 26
(√50 - √18)/√2 = [√(25 *2) - √(9 * 2)]/√2 = (5√2 - 3√2)/√2 = 2√2/√2 = 2
Odp: B
zad 27
(√3 - √27 + √243)/√3 = [√3 - √(9 *3) + √(81 * 3)]/√3 =
= (√3 - 3√3 + 9√3)/√3 = 7√3/√3 =7
Odp: C
zad 28
(3¹⁰ * 3²⁰)⁶ = (3¹⁰⁺²⁰)⁶ = (3³⁰)⁶ = 3¹⁸⁰ = (3³)⁶⁰ =27⁶⁰
Odp: A
zad 29
I. (- 2)³ = - 8
II. √49 - ∛64 = 7 - 4 = 3
III. 1 : (1/3)² = 1 : 1/9 = 1 * 9 = 9
IV. (- 1,7)² = 2,89
Odp: C
zad 30
3⁶ * 27¹² * 81²⁵ = 3⁶ * (3³)¹² * (3⁴)²⁵ = 3⁶ * 3³⁶ * 3¹⁰⁰ = 3⁶⁺³⁶⁺¹⁰⁰ = 3¹⁴² =
= (3²)⁷¹ = 9⁷¹
Odp: D
zad 31
3⁸⁾³ * ∛9² = 3⁸⁾³ * 9²*¹⁾³ =3⁸⁾³ * 9²⁾³ =3⁸⁾³ *(3²)²⁾³ =3⁸⁾³ * 3⁴⁾³ = 3⁸⁾³⁺⁴⁾³ =
= 3¹²⁾³ = 3⁴
Odp: C
zad 32
2⁴⁾³ * ∛4⁴ =2⁴⁾³ * (4⁴)¹⁾³ = 2⁴⁾³ * (2²)⁴⁾³ = 2⁴⁾³ * 2⁸⁾³ = 2⁴⁾³⁺⁸⁾³ = 2¹²⁾³ = 2⁴
Odp: B
zad 33
7⁴⁾³ * ∛7⁵ = 7⁴⁾³ * (7⁵)¹⁾³ = 7⁴⁾³ * 7⁵⁾³ = 7⁴⁾³⁺⁵⁾³ = 7⁹⁾³ = 7³
