Odpowiedź:
[tex]\dfrac{27^{9}+81^{7}}{9^{13}} = \dfrac{(3^{3})^{9}+(3^{4})^{7}}{(3^{2})^{13}} = \dfrac{3^{27}+3^{28}}{3^{26}} = \dfrac{3^{26}\cdot3+3^{26}\cdot3^{2}}{3^{26}} = \dfrac{3^{26}(3+3^{2})}{3^{26}} =\\\\\\= 3+3^{2} = 3+9 = \boxed{12}[/tex]
Szczegółowe wyjaśnienie:
[tex](a^{m})^{n} = a^{m\cdot n}[/tex]
Odpowiedź:
[tex]\cfrac{27^9+81^7}{9^{13}}=\cfrac{\left(3^3\right)^9+\left(3^4\right)^7}{\left(3^2\right)^{13}}=\cfrac{3^{27}+3^{28}}{3^{26}}=\cfrac{3^{27}}{3^{26}}+\cfrac{3^{28}}{3^{26}}=3^1+3^2=3+9=\boxed{12}[/tex]