Odpowiedzi

  • Użytkownik Zadane
2009-11-08T14:25:24+01:00
1.
a)
-2⁻³=-(1/2)³=-1/8
(-3)⁻²=(-1/3)²=1/27
-4⁻⁴=-(1/4)⁴=-1/64
b)
(3/5)³=(5/3)³=(125/27)
(2/3)⁻²=(3/2)²=9/4
2/[7⁻¹]=2/[1/7]=2:(1/7)=2*(7/1)=14
(-1/6)⁻²=(-6/1)²=(-6)²=36
c)
0,1⁻⁴=(1/10)⁻⁴=(10/1)⁴=10⁴=10000
0,3⁻³=(3/10)⁻³=(10/3)³=1000/27
(-0,2)⁻²=(-2/10)⁻²=(-10/2)²=(-5)²=25
(-0,4)⁻¹=(-4/10)⁻¹=(-10/4)¹=(-10/4)=-2,5
d)
(1 i 1/2)⁻²=(3/2)⁻²=(2/3)²=4/9
(-2 i 1/3)⁻³=(-7/3)⁻³=(-3/7)³=-27/343
(-3 i 1/4)⁻²=(-13/4)⁻²=(-4/13)²=16/169
(4 i 1/5)⁻¹=(21/5)⁻¹=(5/21)¹=5/21
2.
a) 3⁻³ * (1/9)⁻³ = 3⁻³ * ( 3 ⁻²)⁻³ = 3⁻³ * 3⁶ = 3⁻³⁺⁶ = 3³=27
b) 5⁻¹ * (1/125)⁻¹ = 5⁻¹ * (5 ⁻³)⁻¹ = 5⁻¹ * 5³= 5⁻¹⁺³=5²=25
c) (2/3)⁻² * (3/4)⁻² = (3/2)² * (4/3)² = [ (3/2) * (4/3) ]² = 2²=4
d) (2,8)⁻⁴ * (5/14)⁻⁴ = (28/10)⁻⁴ * (5/14)⁻⁴ = (10/28)⁴ * (14/5)⁴ = [(10/28) * (14/5)]⁴ = 1⁴ =1
2009-11-08T14:40:52+01:00
Zad 1.
a) -8 b) - 27/125 c) 0,0001 d) 9/4
-27 4/3 -0,027 - 343/27
256 2/-7 0,04 169/16
1/36 -0,4 -21/5

zad 2.
a) - 1/27
b) / 1/25
c) 1/4
d)1
2009-11-08T15:08:22+01:00
A)
-2⁻³=-(½)³=-1/8
(-3)⁻²=(-1/3)²=1/9
-4⁻⁴=-(1/4)⁴=-1/256
b)
(3/5)⁻³=(5/3)³=125/27=4¹⁷/₂₇
2⁻²₋(½)²₋¼
''''''₋ ''''''''' ₋''''''' te kropki to kreska ułamkowa pod kreska liczba 3
3 3 3
2 2 2
'''''='''''''=''''''
7⁻¹ 1/7¹ 1/7
(-1/6)⁻²=(-6)²=36
c)
(0,1)⁻⁴=(1/10)⁻⁴=10⁴=10000
(0,3)⁻³=(3/10)⁻³=(10/3)³=1000/27=37¹/₂₇
(-0,2)⁻²=(-2/10)⁻²=(-5)²=25
(-0,4)⁻¹=(-4/10)⁻¹=(-10/4)¹=-2,5

(1½)⁻²=(³/₂)⁻²=(2/3)²=4/9
(-2¹/₃)⁻³=(-⁷/₃)⁻³=(-3/7)³=-²⁷/₃₄₃
(-3¼)⁻²=(-¹³/₄)⁻²=(-⁴/₁₃)²=¹⁶/₁₆₉
(4¹/₅)⁻¹=(²¹/₅)⁻¹=(⁵/₂₁)¹=5/21

3⁻³×(1/9)⁻³=(1/3)³×9³=¹/₉×729=81
5⁻¹×(¹/₁₂₅)⁻¹=¹/₅×125=25
(²/₃)⁻²×(¾)⁻²=(³/₂)²×(⁴/₃)²=⁹/₄×¹⁶/₉=4
(2,8)⁻⁴×(⁵/₁₄)⁻⁴=(²⁸/₁₀)⁻⁴×(¹⁴/₅)⁴=(¹⁰/₂₈)⁴×(¹⁴/₅)⁴=
=¹⁰⁰⁰⁰/₆₁₄₆₅₆ × ³⁸⁴¹⁶/₆₂₅=1