Question

Scrie ca putere:

a) 2 la puterea 53 :2 la puterea 40
b) 7 la puterea 11 : 7
c) 9 la puterea 12 : 9 la puterea 3
d) 2 la puterea 83 : 2 la puterea 70
e) 2 la puterea 70: 8 la puterea 23
f) 3 la puterea 60 : 81 la puterea 15
g) (2 la puterea 7) la puterea 10
h) (5 la puterea 3) la puterea 4
i) 2 la puterea 20*5 la puterea 20
j) 12 la puterea 30:6 la puterea 30

Dau coroana

Answer 1

Răspuns:

a) 2 la puterea 53 :2 la puterea 40

2⁵³ : 2⁴⁰ = 2⁽⁵³⁻⁴⁰⁾ = 2¹³

b) 7 la puterea 11 : 7

7¹¹ : 7 = 7⁽¹¹⁻¹⁾ = 7¹⁰

c) 9 la puterea 12 : 9 la puterea 3  

9¹² : 9³ = 9⁽¹²⁻³⁾ = 9⁹

d) 2 la puterea 83 : 2 la puterea 70

2⁸³ : 2⁷⁰ = 2⁽⁸³⁻⁷⁰⁾ = 2¹³

e) 2 la puterea 70: 8 la puterea 23

2⁷⁰ : 8²³ = 2⁷⁰ : (2³)²³ = 2⁷⁰ : 2⁽³ˣ²³⁾ = 2⁷⁰ : 2⁶⁹ = 2⁽⁷⁰⁻⁶⁹) = 2¹ = 2

f) 3 la puterea 60 : 81 la puterea 15

3⁶⁰ : 81¹⁵ = 3⁶⁰ : (3⁴)¹⁵ = 3⁶⁰ : 3⁽⁴ˣ¹⁵⁾ = 3⁶⁰ : 3⁶⁰ = 3⁽⁶⁰⁻⁶⁰⁾ = 3⁰ = 1

g) (2 la puterea 7) la puterea 10

(2⁷)¹⁰ = 2⁽⁷ˣ¹⁰⁾ = 2⁷⁰

h) (5 la puterea 3) la puterea 4

(5³)⁴ = 5⁽³ˣ⁴⁾ = 5¹²

i) 2 la puterea 20*5 la puterea 20

2²⁰ x 5²⁰ = (2 x 5)²⁰ = 10²⁰

j) 12 la puterea 30:6 la puterea 30

12³⁰ : 6³⁰ = (12 : 6)³⁰ = 2³⁰