Question

Zad.3 Na miejsce kropek wstaw znak > lub <.

a) 3⁻² ... 4⁻³

b) (⅓)⁻⁴ ... (½)⁻⁵

c) (0.75)⁻³ ... (⅔)⁻⁴

d) (1⅔)⁻² ... (2½)⁻³

e) (0.1)⁻⁴ ... (0.04)⁻²

f) (2,6) ⁻² ... (1,75)⁻²

Zad.4

a) (3⁻¹+3)⁻¹

b) 2⁻³/3⁻² : 4⁻³/9⁻¹

Answer 1

Zadanie 4

a) 3⁻² > 4⁻³

3⁻²=(1/3)²=1/9

4⁻³=(1/4)³=1/64

 

b) 

(⅓)⁻⁴ > (½)⁻⁵

(⅓)⁻⁴=3⁴=81

(½)⁻⁵=2⁵=32

 

c)

 (0.75)⁻³ < (⅔)⁻⁴

 (0.75)⁻³=(75/100)⁻³=(3/4)⁻³=(4/3)³=64/27 = 2 10/27

 (⅔)⁻⁴=(3/2)⁴=81/16=5 1/16

 

d) (1⅔)⁻² > (2½)⁻³  

(1⅔)⁻²=(5/3)⁻²=(3/5)²=9/25=45/125

(2½)⁻³=(5/2)⁻³=(2/5)³=8/125

 

e) (0.1)⁻⁴ > (0.04)⁻²

(0.1)⁻⁴=(1/10)⁻⁴=10⁴=10000

(0.04)⁻²=(4/100)⁻²=(100/4)²=25²=625

 

f) (2,6) ⁻² < (1,75)⁻²

(2,6) ⁻²=(26/10)⁻²=(13/5)⁻²=(5/13)²=25/169

(1,75)⁻²=(175/100)⁻²=(100/175)²=(4/7)²=16/49

 

Zadanie 4

a) (3⁻¹+3)⁻¹=(1/3+3)⁻¹=(3 1/3)⁻¹=(10/3)⁻¹=3/10=0,3

 

b) 2⁻³/3⁻² : 4⁻³/9⁻¹=(1/2)³/(1/3)²:(1/4)³/1/9=1/8/1/9 : 1/64/1/9=

1/8*9 : 1/64*9=9/8:9/64=9/8*64/9=8