Question

Scrieti ca puteri cu aceeasi baza 2^16 si 8^4 si (8/27)^3 si (4/9)^5 Vreau explicatie daca se poate .
Scrieti ca puteri care au acelasi exponent 4^15 si 3^10 ; (1/4)18 si (3/5)^36 La fel cu explicatie dataliata .
MULTUMESC !

Answer 1

Răspuns:

Explicație pas cu pas:

2¹⁶  = 2¹⁶

8⁴ = (2³)⁴ = 2³ˣ⁴ = 2¹²  

(8/27)³ = (2³/3³)³ = [(2/3)³]³ = (2/3)³ˣ³ = (2/3)⁹

(4/9)⁵ = (2²/3²)⁵ = [(2/3)²]⁵ = (2/3)²ˣ⁵ = (2/3)¹⁰  

4¹⁵ = (2²)¹⁵ = 2²ˣ¹⁵ = 2³⁰ = 2³ˣ¹⁰ = (2³)¹⁰ = 8¹⁰

3¹⁰ = 3¹⁰

(1/4)¹⁸  = (1/4)¹⁸

(3/5)³⁶ = (3/5)²ˣ¹⁸ = [(3/5)²]¹⁸ = (3²/5²)¹⁸ = (9/25)¹⁸