Rozwiązane

1.Która z tych liczb jest większa.Podaj obliczenia:
a)2⁵ czy 5²
b)(-2)⁵ czy (-5)²
c)(⅓)² czy (½)³
2.Oblicz i podaj obliczenia:
a)2⁻²
b)3⁻³
c)(-2)⁻²
d)(¾)⁻³
e)(6¼)⁻²
f)(⅛)⁻¹
g)(-1½)⁻¹
h)1,8⁻³
i)1,2⁻³
j)4,5⁰
k)(-7)¹
l)0¹

Odpowiedź :

1.Która z tych liczb jest większa.Podaj obliczenia:
a)2⁵=2*2*2*2*2=4*4*2=16*2=32
5²=5*5=25, zatem 2⁵>5²
b)(-2)⁵=(-2)*(-2)*(-2)*(-2)*(-2)=-32
(-5)²=(-5)*(-5)=25, zatem (-5)²> (-2)⁵
c)(⅓)²=(1/3)*(1/3)=1/9=(8/72)
(½)³=(1/2)*(1/2)*(1/2)=(1/8)=(9/72)
zatem (1/2)³>(1/3)²
2.Oblicz i podaj obliczenia:
a)2⁻²=(1/2)²=(1/2)*(1/2)=(1/4)
b)3⁻³=(1/3)³=(1/3)*(1/3)*(1/3)=(1/27)
c)(-2)⁻²=(-1/2)²=(-1/2)*(-1/2)=(1/4)
d)(¾)⁻³=(4/3)³=(4/3)*(4/3)*(4/3)=(64/9)=7 i 1/9
e)(6¼)⁻²=(25/4)⁻²=(4/25)²=(4/25)*(4/25)=(16/625)
f)(⅛)⁻¹=(8/1)¹=8¹=8
g)(-1½)⁻¹=(-3/2)⁻¹=(-2/3)¹=-2/3
h)1,8⁻³=(1 i 8/10)⁻³=(18/10)⁻³=(10/18)³=(10/18)*(10/18)*(10/18)=(1000/5832)
i)1,2⁻³=(1 i 2/10)⁻³=(12/10)⁻³=(10/12)³=(10/12)*(10/12)*(10/12)=1000/1728
j)4,5⁰=1
k)(-7)¹=-7
l)0¹ =0
1.
a) 2⁵= 2×2×2×2×2 = 32
5²= 5×5= 25
2⁵>5²

b) (-2)⁵= -32
(-5)²= 25
(-2)⁵<(-5)²

c)(⅓)² = ¼
(½)³ = ⅛
(⅓)² >(½)³

2.
a)2⁻²= 1/(2)₂\= ¼
b)3⁻³ = 1/ (3)³= 1/27
c)(-2)⁻²= 1/(-2)²=¼
d)(¾)⁻³= 1/(3/4)³= 1/ (27/64)= 64/27
e)(6¼)⁻²= 1/ (25/4)²= 1/ (625/16) = 16/625
f)(⅛)⁻¹ = 8
g)(-1½)⁻¹ = -5/2
h)1,8⁻³ = (18/10)⁻³=1/(9/5)³= 1/(729/125)= 125/729
i)1,2⁻³ = 1/(6/5)³= 1/(216/125)= 125/216
j)4,5⁰ = 1
k)(-7)¹ = -1/7
l)0¹ = 0

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