Odpowiedź:
1.
a) 3√14 * 2√3 = 3 * 2√(14 * 3) = 6√42
b) 2√5 - √3 + 2√3 + 6√5 = 8√5 + √3
c) 10√15 : 2√3 = 10/2√(15/3) = 5√5
d) 2√24 - 3√54 = 2√(4 * 6) - 3√(9 * 6) = 2 * 2√6 - 3 * 3√6 = 4√6 - 9√6 = - 5√6
e) 4⁷ * 8⁵ : 16⁴ = (2²)⁷ * (2³)⁵ : ( 2⁴)⁴ = 2¹⁴ * 2¹⁵ : 2¹⁶ = 2¹⁴⁺¹⁵⁻¹⁶ = 2⁻¹⁵
f) (27⁶ * 9⁵)/3⁴ = [(3³)⁶ * (3²)⁵]/3⁴ = (3¹⁸ * 3¹⁰)/3⁴ = 3¹⁸⁺¹⁰/3⁴ = 3²⁸/3⁴ = 3¹⁸⁻⁴ =3¹⁴
g) 6⁵/(32 * 9²) = (2⁵ * 3⁵)/(2⁵ * 3⁴) = 2⁵/2⁵ * 3⁵/3⁴ = 1 * 3⁵⁻⁴ = 1 * 3¹ = 3
h) 4 1/3 - 1 1/2 * 4/5 = 4 1/3 - 3/2 * 4/5 = 4 1/3 - 3 * 2/5 = 4 1/3 - 6/5 = 4 1/3 - 1 1/5 =
= 4 5/15 - 1 3/15 = 3 2/15
i) ∛(3 3/8) - 0,5 * 2 1/2 = ∛(27/8) - 1/2 * 5/2 = 3/2 - 5/4 = 6/4 - 5/4 = 1/4
