Expresia din paranteză poate fi simplificată:
[tex]\it \dfrac{1}{\not7}\cdot\dfrac{\not7}{35}\cdot\dfrac{14\not0}{700}\cdot\dfrac{7}{1\not0}\cdot\dfrac{10^2}{2^2}=\dfrac{1}{35}\cdot\dfrac{14}{700}\cdot\dfrac{7}{1}\cdot\dfrac{100}{4}=\dfrac{14}{35}\cdot\dfrac{700}{700}\cdot\dfrac{1}{4}=\dfrac{14}{140}=\dfrac{1}{10}[/tex]
Egalitatea din enunț devine:
[tex]\it\left(\dfrac{1}{10}\right)^n=\dfrac{1}{100} \Rightarrow \dfrac{1}{10^n}=\dfrac{1}{10^2}\Rightarrow n=2.[/tex]
