Question

compara puterile 2 la 150 si 3 la 90

Answer 1

Calculam cmmdc(150,90)
90/2
45/5
9/3
3/3
1
90=3^2*5^1*2^1
150/3
50/5
10/5
2/2
1/
150=3^1*5^2*2^1
Se iau toti factorii primi comuni, la puterile cele mai mici.
cmmdc(90,150)=3^1*5^1*2^1=3*5*2=3*10=30
Deci:
[tex]2^{150}=2^{5*30}=(2^{5})^{30}=32^{30}\\ 3^{90}=3^{3*30}=(3^{3})^{30}=27^{30}\\32^{30}\ \textgreater \ 27^{30}\\2^{150}\ \textgreater \ 3^{90}[/tex]