Odpowiedź:
zad 4
a)
32² * 2⁷ =(2⁵)² * 2⁷ = 2¹⁰ * 2⁷ = 2¹⁰⁺⁷ = 2¹⁷
b)
125⁴ : 25⁴ = (5³)⁴ : (5²)⁴ = 5¹² : 5⁸ = 5¹²⁻⁸ = 5⁴
c)
(3 * 9⁵)/(27² * 9) = [3 * (3²)⁵]/[(3³)² * 3²] = (3 * 3¹⁰)/(3⁶ * 3²) = 3¹⁺¹⁰/3⁶⁺² =
= 3¹¹/3⁸ = 3¹¹⁻⁸ = 3³
d)
(1/3)² * (1/9)³ : 1/27 = (1/3)² * [(1/3)²]³ : (1/3)³ = (1/3)² * (1/3)⁶ : (1/3)³ =
= (1/3)²⁺⁶⁻³ = (1/3)⁵
e)
3 * 2⁴ + 4² = 3 * 2⁴ + (2²)² = 3 * 2⁴ + 2⁴ = 2⁴(3 + 1) = 2⁴ * 4 = 2⁴ * 2² =
= 2⁴⁺² = 2⁶
f)
7 * 5⁶ - 2 * 25³ = 7 * 5⁶ - 2 * (5²)³ = 7 * 5⁶ - 2 * 5⁶ = 5⁶(7 - 2) =
= 5⁶ * 5 = 5⁶⁺¹ = 5⁷
g)
[(2³)² * 3³ + 15 * 3² - 5 * 27]/(3² * 2) = [2⁶ * 3³ + 15 * 3² - 5 * 3³)/(3³ * 2) =
= 3²(2⁶ * 3 + 15 - 5 * 3)/(3³ * 2) = 3²(2⁶ * 3 + 15 - 15)/(3³ * 2) =
= 3²(2⁶ * 3)/(3³ * 2) = (3³ * 2⁶ )/(3³ * 2) = 3³/3³ * 2⁶/2 = 1 * 2⁶⁻¹ = 2⁵
