Question

18. Ordonaţi crescător numerele a)2³⁵,4¹⁸ b)3⁶¹,9²⁹,27²⁰ c)625⁴125¹⁵,25²⁰,5³⁹​

Answer 1

➪ Ordonaţi crescător numerele:

a) 2³⁵, 4¹⁸

☂︎ Aducem puterile la aceeași bază.

4¹⁸ = (2²)¹⁸ = 2³⁶

• Crescător: 2³⁵ < 2³⁶

2³⁵ < 4¹⁸

b) 3⁶¹, 9²⁹, 27²⁰

9²⁹ = (3²)²⁹ = 3⁵⁸

27²⁰ = (3³)²⁰ = 3⁶⁰

• Crescător: 3⁵⁸< 3⁶⁰< 3⁶¹

9²⁹< 27²⁰< 3⁶⁰

c) 625⁴, 125¹⁵, 25²⁰, 5³⁹

625⁴ = (5⁴)⁴ = 5¹⁶

125¹⁵ = (5³)¹⁵ = 5⁴⁵

25²⁰ = (5²)²⁰ = 5⁴⁰

• Crescator: 5¹⁶< 5³⁹< 5⁴⁰< 5⁴⁵

625⁴ < 5³⁹ < 25²⁰ < 125¹⁵

꧁ADE꧂

Answer 2

Răspuns

A) 2 ^35, 2 ^36

B) 3 ^58, 3 ^60, 3 ^61

C) 5 ^16, 5 ^39, 5 ^40, 5^45

Explicație pas cu pas de

A)

4 ^18 =(2 ^2) ^18 =2 ^(2 ×18) =2 ^36

2 ^35, 2 ^36

2 ^35, 4 ^18

B)

9 ^29 =(3 ^2) ^29 =3 ^(2 ×29) =3 ^58

27 ^20 =(3 ^3) ^20 =3 ^(3 ×20) =3 ^60

3 ^58, 3 ^60, 3 ^61

9 ^29, 27 ^20, 3 ^61

C)

625 ^4 =(5 ^4) ^4 =5 ^(4 ×4) =5 ^16

125 ^15 =(5 ^3) ^15 =5 ^(3 ×15) =5 ^45

25 ^20 =(5 ^2) ^20 =5 ^(2 ×20) =5 ^40

5 ^16, 5 ^39, 5 ^40, 5 ^45

625 ^4, 5 ^39, 25 ^20, 125 ^15