Zad 1. Oblicz
a) pierwiastek sześcienny z 6 do potegi 3
b) w nawiasie pierwiastek z 6 do potegi 4
c) w naiwasie pierwiastek szescienny z 12 do potegi 3
d) w nawiasie pierwiastek z 3 do potegi -2
Zad 2. Oblicz
a) (1/5)do potegi -1 + (1/5) do potegi -2
b) (1/3 -1/2)do potegi -1
c) (1/3 - 1/5)do potegi -3 : (1/5 +1/3)do potegi -3
d) (-6)do -2 * (1/6)do potegi -4
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Zad 1. Oblicz
Jeżeli piewiastek 3 stopnia z jakiejś liczby podniesimy do potęgi 3, to wynikiem jest liczba pod pierwiastkiem
(√6)⁴ = (6⁴)¹/² = 6²
a) pierwiastek sześcienny z 6 do potegi 3
∛(6³) = (∛6)³ = 6
b) w nawiasie pierwiastek z 6 do potegi 4
(√6)⁴ = (6⁴)¹/²= 6²
c) w naiwasie pierwiastek szescienny z 12 do potegi 3=
= (∛12)³ = 12
d) w nawiasie pierwiastek z 3 do potegi -2 =
= (√3)⁻² = [( 3)¹/²]⁻² = 3 ⁻¹ = 1/3
Zad 2. Oblicz
a) (1/5)do potegi -1 + (1/5) do potegi -2 =
=(1/5)⁻¹ + (1/5)⁻² =
= 5¹ + 5² =
= 5 + 25 =
= 30
b) (1/3 -1/2)do potegi -1 =
= (2/6 - 3/6)⁻¹ =
= (-1/6)⁻¹ =
= (-6)¹ =
= -6
c) (1/3 - 1/5)do potegi -3 : (1/5 +1/3)do potegi -3 =
= (5/15 - 3/15 )⁻³ : ( 3/15 + 5/15)⁻³ =
= (2/15)⁻³ : ( 8/15)⁻³ =
= (15/2)³ : ( 15/8)³ =
= [ (15/2) : (15/8) ]³ =
= [ (15/2 )*(8/15) ]³ =
= 4³ =
= 64
d) (-6)do -2 * (1/6)do potegi -4 =
= (-6)⁻² *(1/6)⁻⁴ =
= (-1/6)² *(1/6)⁻⁴ =
= (1/6)² *(1/6)⁻⁴ =
= (1/6)⁻² =
= 6² =
=36
Uwaga:
(-1/2)² = (1/2)² = 1/4 przy parzystych potęgach
(-1/2)³ = -( 1/2)³ = - 1/8 przy potęgach nieparzystych
a)=
b)=
c)
d)=
a)=
b)=(
c)=
d)=