[tex]a)\ \ 27^5=(3^3)^5=3^{15}\\\\\\b)\ \ 81\cdot3^5=3^4\cdot3^5=3^{4+5}=3^9\\\\\\c)\ \ \dfrac{9^5}{3^8}=\dfrac{(3^2)^5}{3^8}=\dfrac{3^1^0}{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^{18}\\\\\\e)\ \ 27^8:9^6=(3^3)^8:(3^2)^6=3^{24}:3^{12}=3^{24-12}=3^{12}\\\\\\f)\ \ \dfrac{3^1^0\cdot27}{9^5}=\dfrac{3^1^0\cdot3^3}{(3^2)^5}=\dfrac{3^{10+3}}{3^1^0}=\dfrac{3^1^3}{3^1^0}=3^{13-10}=3^3[/tex]
[tex]g)\ \ (27^2)^5\cdot9=27^1^0\cdot3^2=(3^3)^{10}\cdot3^2=3^{30}\cdot3^2=3^{30+2}=3^{32}\\\\\\h)\ \ \left(\dfrac{9^4}{27}\right)^2=\left(\dfrac{(3^2)^4}{3^3}\right)^2=\left(\dfrac{3^8}{3^3}\right)^2=(3^{8-3})^2=(3^5)^2=3^{10}\\\\\\Zastosowane\ \ wzory\\\\(a^m)^n=a^{m\cdot n}\\\\a^m\cdot a^n=a^{m+n}\\\\\frac{a^m}{a^n}=a^{m-n}[/tex]
