Taller de Repaso 3

NIVEL 1 :

1. a) 2.2.2.2.2 = 2^5

b) (-3).(-3).(-3).(-3) = 〖(-3)〗^4

c) 1/2.1/2.1/2 = 〖(1/2)〗^ 3

2. 5^2 → exponente
↓
base

〖(-3)〗^5 → exponente
↓
base

〖(4/5)〗^5 → exponente
↓
base

〖(-1/2)〗^3 → exponente
↓
base

〖-4〗^2 → exponente
↓
base

-〖(2/5)〗^4 → exponente
↓
base

3. a) 3^3 = 27

b)〖(-5)〗^3 = -125

c)〖(-5)〗^2 = 25

d)〖(1/3)〗^3 = 1/27

e)〖(2/3)〗^2 = 4/9

4. a)〖(-7)〗^3 = -343

b)〖(4/5)〗^2 = 16/25

c)〖(-2/3)〗^2 = 4/9

d)〖-6〗^4 = 1296

e)〖(5/6)〗^1 = 5/6

5. a) 5^2.5^5.5^4 = 5^11

(-2)^3.(-2)^4.(-2)^5 = (-2)^12

(1/5)^3.(1/5)^7.(1/5)^8 = (1/5)^18

b) 8^6 : 8^4 = 8^6-4 = 8^2 = 64

(4/5)^7 : (4/5)^3 = (4/5)^7-3 = (4/5)^4

(-9)^5 : (-9)^2 = (-9)^5-2 = (-9)^3

c) (5^2)^3 = 5^6

[(-2)^3]^4 = (-2)^12

[(2/5)^2]^6 = (2/5)^12

d) 3^2.2^2 = 6^2

(-5)^3.(2)^3 = (-10)^3

(3/5)^2.(5/4)^2 = (15/20)^2

e) 8^3 : 4^3 = 2^3

(2/3)^3 : (4/9)^3 = (18/12)^3

(6)^2 : (-3)^2 = (-2)^2

6. a) 2^3 + 3^2 - 5^2 = 8 + 9 - 25 = -10

b) (2/3)^3 - (1/2)^4 + (5/6)^2 = 8/27 - 1/6 + 25/36 = 12 - 27 + 675/432 =

776/432

c) (-3)^2 - (2/3)^3 + (-1/2)^2 = 9/1 - 8/27 + 1/4 = 972 - 32 + 27/108 = 967/108


7. a) √49 = +7 y (-7),porque (+7)^2 = 49 y (-7)^2 = 49

b) √121 = +11 y (-11), porque (+11)^2 = 121 y (-11)^2 = 121

c) √-25 = √25.√-1 = 5i

d) √4/16 = 2/4 y (-2/-4) simplificando quedaría 1/2

e) √-36/4 = 6/2 y (-6/-2)simplificando quedaría 3/1 = 3