Question

Comparati numerele : 108⁷² 100¹°⁸ .   P.S. dau coroana.

Answer 1

[tex]a=108^{72}=108^{2\cdot 36}=(108^2)^{36}=11664^{36}\\ b=100^{108}=100^{3\cdot 36}=(100^3)^{36}=1000000^{36}\\ b\ \textgreater \ a[/tex]

Observatie: Am folosit formula:$a^{b\cdot c}=(a^b)^c$

Answer 2

$108^{72}=( 108^{2})^{36}=(108*108)^{36} \to 11664^{36} \\ 100^{108}=( 100^{3})^{36}=(100*100*100)^{36} \to 1000000^{36} \\ 100^{108}\ \textgreater \ 108^{72}$