Rozwiązane

Oblicz sprytnie :

c) (4/9)⁷:(2/9)⁸
d) (13/9)⁵:(13/3)⁴



Odpowiedź :

c) (4/9)⁷:(2/9)⁸=
= (4/9)⁷:(2/9)⁸=
=(4/9)⁷:[(2/9)⁷*2/9]=
=(4/9*9/2)⁷*9/2=
=2⁷*9/2=2⁶*9=64*9=576

d) (13/9)⁵:(13/3)⁴=
= 13/9(13/9)⁴:(13/3)⁴=
=13/9*(13/9*3/13)⁴=
=13/9*(1/3)⁴ =
=13/729
c) (4/9)⁷:(2/9)⁸ = (4/9)⁷:[(2/9)⁷*2/9]= (4/9*9/2)⁷*9/2 = 2⁷*9/2 = 2⁶*9 = 64*9= 576

d) (13/9)⁵:(13/3)⁴ = (13/9)¹*(13/9)⁴:(13/3)⁴ = 13/9*(13/9*3/13)⁴ = 13/9*(⅓)⁴ = 13/9*1/81 = 13/729
Mirej
1) (4/9)⁷:(2/9)⁸ = (4/9)⁷:((2/9)⁷ × 2/9) = (4/9*9/2)⁷ × 9/2 = 2⁷ × 9/2 = 2⁶ × 9 = 64 × 9 = 576

2) (13/9)⁵:(13/3)⁴ = 13/9 × (13/9)⁴:(13/3)⁴ = 13/9 × (13/9 × 3/13)⁴ = 13/9 × (1/3)⁴ = 13/729

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