Răspuns:
Explicație pas cu pas:
a) 2⁴⁵ ; 3²⁷ ; 4¹⁸
2⁴⁵ = 2⁵ˣ⁹ = (2⁵)⁹ = 32⁹
3²⁷ = 3³ˣ⁹ = (3³)⁹ = 27⁹
4¹⁸ = 4²ˣ⁹ = (4²)⁹ = 16⁹ =>
16⁹ < 27⁹ < 32⁹ => 4¹⁸ < 3²⁷ < 2⁴⁵
b) 2⁵⁶ ; 5²⁴ ; 3³²
2⁵⁶ = 2⁷ˣ⁸ = (2⁷)⁸ = 128⁸
5²⁴ = 5³ˣ⁸ = (5³)⁸ = 125⁸
3³² = 3⁴ˣ⁸ = (3⁴)⁸ = 81⁸ =>
81⁸< 125⁸ < 128⁸ => 3³² < 5²⁴ < 2⁵⁶
c) 5⁴⁴ ; 3⁶⁶ ; 2¹¹⁰
5⁴⁴ = 5²ˣ²² = (5²)²² = 25²²
3⁶⁶ = 3³ˣ²² = (3²)²² = 9²²
2¹¹⁰ = 2⁵ˣ²² = (2⁵)²² = 32²² =>
9²² < 25²² < 32²² => 3⁶⁶ < 5⁴⁴ < 2¹¹⁰
d) 5¹³ ; 3³⁵ ; 12¹⁰
5¹³ = 5²ˣ⁵⁺³ = 5³·(5²)⁵ = 5³·25⁵ = 125⁵:25
3³⁵ = 3⁷ˣ⁵ = (3⁷)⁵ = 2187⁵
12¹⁰ = 12²ˣ⁵ = (12²)⁵ = 144⁵
5³·25⁵ < 144⁵ < 2187⁵ => 5¹³ < 12¹⁰ < 3³⁵
e) 9³³ ; 3⁵² ; 27¹⁹
9³³ = (3²)³³ = 3²ˣ³³ = 3⁶⁶
3⁵²
27¹⁹ = (3³)¹⁹ = 3³ˣ¹⁹ = 3⁵⁷ =>
3⁵² < 3⁵⁷ < 3⁶⁶ => 3⁵² < 27¹⁹ < 9³³
f) 5⁴⁴ ; 25²⁹ ; 625¹¹
5⁴⁴
25²⁹ = (5²)²⁹ = 5²ˣ²⁹ = 5⁵⁸
625¹¹ = (5⁴)¹¹ = 5⁴ˣ¹¹ = 5⁴⁴
5⁴⁴ = 5⁴⁴ < 5⁵⁸ => 5⁴⁴ = 625¹¹ < 25²⁹
