Răspuns:
[tex] \frac{1}{16}[/tex]
Explicație pas cu pas:
Stim ca: [tex](\frac{x}{y} )^z=\frac{x^z}{y^z}[/tex].
Folosim aceasta relatie si avem:
[tex](\frac{3}{7})^{4}*(\frac{49}{36}) ^2=\frac{3^4}{7^4} *\frac{49^2}{36^2}[/tex]
Stim ca 49=7², iar 36=6².
Si mai stim si ca: [tex](a^b)^c=a^{bc}[/tex].
Folosim aceste relatii si obtinem:
[tex]\frac{3^4}{7^4} *\frac{49^2}{36^2}=\frac{3^4}{7^4}* \frac{(7^2)^2}{(6^2)^2}=\frac{3^4}{7^4} *\frac{7^4}{6^4} =Simplificam~7^4=\frac{3^4}{6^4}[/tex]
Si folosim prima regula scrisa in exercitiu (de doua ori):
[tex]\frac{3^4}{6^4}=(\frac{3}{6}) ^4=Simplificam~3~cu~6=(\frac{1}{2})^4=\frac{1^4}{2^4} =\frac{1}{16}[/tex]
