Question

EXERCITII CU RIDICAREA PUTERILOR CU EXPONENT NATURAL AL UNUI NUMAR NATURAL
Determinati numarul x astfel incat:

a) [2⁵*(2*3)⁷] : 3⁷ = 2ˣ

b) (2³*3⁵)²:(2⁴*3⁶):3²=6ˣ

c) 2¹*2²*3³*...*2⁵⁰=2ˣ

Answer 1

a) [2⁵*(2*3)⁷] : 3⁷ = 2ˣ
2⁵*2⁷*3⁷ : 3⁷ = 2ˣ
2¹²*3⁷ : 3⁷ = 2ˣ
2¹² = 2ˣ
x=12

b) (2³*3⁵)²:(2⁴*3⁶):3²=6ˣ
(2⁶*3¹⁰):(2⁴*3⁶):3²=6ˣ
2²*3¹⁰⁻⁶⁻²=6ˣ
2²*3²=6ˣ
6²=6ˣ
x=2

c) 2¹*2²*3³*...*2⁵⁰=2ˣ
2¹⁺²⁺³⁺  ⁺⁵⁰ =2ˣ
x=1+2+3+...+50=50*51/2=1275