Odpowiedź:
zad 11
a)
(2¹³ * 5¹³)/10¹³ = (2 * 5)¹³/10¹³ = 10¹³/10¹³ = 1
b)
(100⁵ : 25⁵)/4⁵ = (100/25)⁵/4⁵ = 4⁵/4⁵ = 1
c)
(1000⁷ : 125⁷)/64³ = (1000/125)⁷/64³ = 8⁷/64³ = 8⁷/(8²)⁷ = 8⁷/8¹⁴ =
= 8⁷⁻¹⁴ = 8⁻⁷ = (1/8)⁷
d)
(17⁴ * 16)/34⁴ = (17/34)⁴ * 16 = (1/2)⁴ * 2⁴ = 2⁻⁴ * 2⁴ = 2⁻⁴⁺⁴ = 2⁰ = 1
e)
(21⁸ * 5⁵)/(15⁵ * 7⁸) = (21/7)⁸ * (5/15)⁵ = 3⁸ * (1/3)⁵ = 3⁸ * 3⁻⁵ = 3⁸⁻⁵ = 3³ = 27
f)
(45⁷ * 4²)/(54⁴ * 5⁷) = (45/5)⁷ * 4²/54⁴ = 9⁷ * (2²)²/54⁴ = 9⁷ * 2⁴/54⁴ =
= 9⁷ * (2/54)⁴ = 9⁷ * (1/27)⁴ = 9⁷ * [(1/3)³]⁴ = (3²)⁷ * (1/3)¹² = 3¹⁴ * 3⁻¹² =
= 3¹⁴⁻¹² = 3² = 9
