Od a) do d) :
[tex]a] \ 27^5=(3^3)^5=3^{3\cdot5}=3^{15}\\\\b] \ 81\cdot3^5=3^4\cdot3^5=3^{4+5}=3^9\\\\c] \ \frac{9^5}{3^8}=\frac{(3^2)^5}{3^8}=\frac{3^{2\cdot5}}{3^8}=\frac{3^{10}}{3^8}=3^{10-8}=3^2\\\\d] \ (3^7\cdot9)^2=(3^7\cdot3^2)^2=(3^{7+2})^2=(3^9)^2=3^{9\cdot2}=3^{18}[/tex]
Od e) do h) :
[tex]e] \ 27^8:9^6=(3^3)^8:(3^2)^6=3^{3\cdot8}:3^{2\cdot6}=3^{24}:3^{12}=3^{24-12}=3^{12}\\\\f] \ \frac{3^{10}\cdot27}{9^5}=\frac{3^{10}\cdot3^3}{(3^2)^5}=\frac{3^{10}\cdot3^3}{3^{10}}=3^3\\\\g] \ (27^2)^5\cdot9=((3^3)^2)^5\cdot3^2=3^{3\cdot2\cdot5}\cdot3^2=3^{30}\cdot3^2=3^{30+2}=3^{32}\\\\h] \ (\frac{9^4}{27})^2=(\frac{(3^2)^4}{3^3})^2=(\frac{3^8}{3^3})^2=(3^5)^2=3^{10}[/tex]
