Odpowiedź:
[tex]a)\ \ \dfrac{5^{27}}{5^{27}-5^{26}}=\dfrac{5^{27}}{5\cdot5^{26}-5^{26}}=\dfrac{5^{27}}{(5-1)\cdot5^{26}}=\dfrac{5^{27}}{4\cdot5^{26}}=\dfrac{5^{27-26}}{4}=\dfrac{5^1}{4}=\\\\\\=\dfrac{5}{4}=1\dfrac{1}{4}[/tex]
[tex]c)\ \ \dfrac{3^{117}\cdot2^{115}}{3^{116}\cdot2^{117}+6^{115}}=\dfrac{3^{117}\cdot2^{115}}{3^{116}\cdot2^{116}\cdot2+6^{115}}=\dfrac{3^{117}\cdot2^{115}}{6^{116}\cdot2+6^{115}}=\dfrac{3^{117}\cdot2^{115}}{6\cdot6^{115}\cdot2+6^{115}}=\\\\\\= \dfrac{3^{117}\cdot2^{115}}{(6\cdot2+1)\cdot6^{115}}=\dfrac{3^{117}\cdot2^{115}}{13\cdot6^{115}}=\dfrac{3^{117}\cdot\not2^{115}}{13\cdot\not2^{115}\cdot3^{115}}=\dfrac{3^{117-115}}{13}=\dfrac{3^2}{13}=\dfrac{9}{13}[/tex]
