Question

Va rog frumos!!! Rezolvati daca puteti problema 8!

Answer 1

(8³⁷ x 81²⁵) / (16²⁷ x 27 ³³) = 
[(2³)37 x (3⁴)²⁵] / [(2⁴)²⁷ x (3³)³³] =
(2¹¹¹ x 3¹⁰⁰) / (2¹⁰⁸ x 3⁹⁹) = 
2⁽¹¹¹⁻¹⁰⁸⁾ x 3⁽¹⁰⁰⁻⁹⁹⁾ = 
2³ x 3¹ = 
8 x 3 =
24

Answer 2

[tex]\it 8^{37} =(2^3)^{37} =2^{3\cdot37} = 2^{111} \\ \\ 81^{25} = (3^4)^{25} = 3^{4\cdot25} = 3^{100} \\ \\ 16^{27} =(2^4)^{27} = 2^{4\cdot27} =2^{108} \\ \\ 27^{33} =(3^3)^{33} = 3^{3\cdot33} = 3^{99} [/tex]

Exercițiul se poate scrie:

$\it \dfrac{2^{111}\cdot3^{100}}{2^{108}\cdot3^{99}} = 2^{111-108} \cdot3^{100-99} = 2^3\cdot3=8\cdot3=24$