Question

Ordonati crescator numerele :

a ) a = 5 ³³ ; b = 2 ⁷⁷
b ) a = 2 ²⁰⁰ ; b = 3 ¹²⁰ si c = 5 ⁸⁰

Answer 1

aducem la aceeasi putere
a) $5^{33}= (5^{3})^{11}=125^{11}$
$2^{77} =(2^{7})^{11}=128^{11}$
$5^{33}<2^{77}$

b) $2^{200}=(2^5)^{40}=32^{40}$
$3^{120}=(3^3)^{40}=27^{40}$
$5^{80}=(5^2)^{40}=25^{40}$
$5^{80}<3^{120}<2^{200}$