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2009-10-31T18:19:44+01:00
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Zad. 009
a)
((2 + 1/3)⁻¹ - 7⁻²)^(-1/2) = ((7/3)⁻¹ - 1/49)^(-1/2) =
(3/7 - 1/49)^(-1/2) = (21/49 - 1/49)^(-1/2) =
(20/49)^(-1/2) = (49/20)^(1/2) = 7/√20 = 7√5 / 10

b)
[27⁵ : 81⁴ - (2⁻¹)⁻³] / [(-9)⁻²] = [(3³)⁵ : (3⁴)⁴ - 2³] / [(-9)⁻²] =
[3¹⁵ : 3¹⁶ - 2³] / [1/81] =[1/3 - 8] / [1/81] =
(1/3 - 24/3) / (1/81) = (-23/3) / (1/81) = 81 * (-23/3) =
27 * (-23) = 621

Zad. 010

= [11/2 - (9/4)⁻²] / [120 - (1/5)⁻³] =
[11/2 - 16/81] / (120 - 125) =
(891/162 - 32/162) / (-5) =
(859 / 162) / (-5) = - 859/810
2009-10-31T18:48:08+01:00
A) ((7/3)⁻¹-7⁻²)⁻¹/²=(3/7-1/49)₋¹/²=(21/49-1/49)⁻¹/²=(20/49)⁻¹/²=(49/20)²= =2401/400=6+1/400

b)(27⁵/81⁴-(2⁻¹)⁻³)÷(-9)⁻²=((3³)⁵/(3⁴)⁴-(1/2)⁻³)÷(-1/9)²=(3¹⁵/3¹⁶-2³)÷(-1/81)=
=(3⁻¹-8)÷(-1/81)=(1/3-8)*(-81)=(-23/3)*(-81)=621