Question

Scrie ca putere:. a)2⁵³:2⁴⁰. b)7¹¹:7. c)9¹²:9³. d)2⁸³:2⁷⁰. e)2⁷⁰:8²³. f)3⁶⁰:81¹⁵. g) (2⁷)¹⁰. h) (5³)⁴. i)2²⁰×5²⁰. j)12³⁰:6³⁰
va rog urgent ​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 2^53 : 2^40 = 2^(53-40) = 2^13

b) 7^11 : 7 = 7^{11-1} = 7^10

c) 9^12 : 9^3 = 9^{12-3} = 9^9

d) 2^83 : 2^70 = 2^{83-70} = 2^13

e) 2^70 : 8^23 = 2^70 : 2^{3*23} = 2^70 : 2^69 = 2^{70-69} = 2^1

f) 3^60 : 81^15 = 3^60 : 3^{4*15} = 3^60 : 3^60 = 1

g) (2^7)^10 = 2^{7*10} = 2^70

h) (5^3)^4 = 5^{3*4} = 5^12

i) 2^20 * 5^20 = (5*2)^20 = 10^20

j) 12^30 : 6^30 = (12:6)^30 = 2^30

Answer 2

Răspuns:

Explicație pas cu pas:

a)  2⁵³ : 2⁴⁰ = 2⁽⁵³⁻⁴⁰⁾ = 2¹³

b) 7¹¹ : 7 = 7⁽¹¹⁻¹⁾ = 7¹⁰

c)  9¹² : 9³ = 9⁽¹²⁻³⁾ = 9⁹

d)  2⁸³ : 2⁷⁰ = 2⁽⁸³⁻⁷⁰⁾ = 2¹³

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

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

g) (2⁷)¹⁰ = 2⁽⁷ˣ¹⁰⁾ = 2⁷⁰

h) (5³)⁴ = 5⁽³ˣ⁴⁾ = 5¹²

i)  2²⁰ x 5²⁰ = (2x5)²⁰ = 10²⁰

j)  12³⁰ : 6³⁰ = (2x6)³⁰ : 6³⁰= 2³⁰ x 6⁽³⁰⁻³⁰⁾ = 2³⁰x1= 2³⁰