Question

1 . Calcule as potências :
a/ (3/7)^-2=
b/ (2/5)^-1=
c/ (1/3)^-3=
d/(-5/4)^-3=
e/(-1/3)^-2=
f/(-2/5)^-3=

2. Resolva as potencias
a/(-4)^-2
b/(+3)^3
c/(-^2/7)^2
d/(+ 3/4)^-4
e /( -1/3)-^2

Answer 1

1 . Calcule as potências :

FRAÇÃO com expoente NEGATIVO
INVERTE a fração e MUDA o SINAL do expoente

a/ (3/7)^-2=


(3/7)⁻² = (7/3)² = 7²/3² = 7x7/3x3 = 49/9

b/ (2/5)^-1= 

(2/5)⁻¹ = (5/2)¹ = 5/2

c/ (1/3)^-3=

(1/3)⁻³ = (3/1)⁺³ = (3/1)³ = 3³ = 3x3x3 = 27

d/(-5/4)^-3= (-4/5)⁺³ = (-4/5)³ = - 4³/5³ = - 4x4x4/5x5x5 = - 64/125
e/(-1/3)^-2= (-3/1)⁺² = (-3/1)² = (-3)² = + 3x3 = + 9

f/(-2/5)^-3= (-5/2)⁺³ = (-5/2)³ = - 5³/2³ = - 5x5x5/2x2x2 = 125/8

2. Resolva as potencias 
a/(-4)^-2 = 
              1              1               1                 1
(-4)⁻² = ------- = ------------ = ---------- = ----------
             (-4)⁺²      (-4)²           +4x4            16

b/(+3)^3

(+3)³ = (3)³ = 3x3x3 = 27

c/(-^2/7)^2

(-2/7)² = + 2²/7² = + 2x2/7x7 = 4/49

d/(+ 3/4)^-4

(+3/4)⁻⁴ = (+4/3)⁺⁴ = (+4/3)⁴ = + 4⁴/3⁴ = 4x4x4x4/3x3x3x3 = 256/81
 
e /( -1/3)-^2 

(-1/3)⁻² = (-3/1)⁺² = (-3)² = + 3x3 = + 9