[tex]d)\ \ \dfrac{(5^2^0+5^1^8)\cdot(3^4)^3}{(5^1^6+5^1^4)\cdot9^5}=\dfrac{5^2\cdot5^1^8+5^1^8\cdot3^1^2}{5^2\cdot5^1^4+5^1^4\cdot(3^2)^5}=\dfrac{(5^2+1)\cdot5^1^8\cdot3^1^2}{(5^2+1)\cdot5^1^4\cdot3^1^0}=\\\\\\=\dfrac{5^1^8\cdot3^1^2}{5^1^4\cdot3^1^0}=5^{18-14}\cdot3^{12-10}=5^4\cdot3^2=625\cdot9=5625[/tex]
[tex]f)\ \ \dfrac{8\cdot3^4\cdot3^1^1-9\cdot3^1^2}{46\cdot(3^1^8:3^4)}=\dfrac{8\cdot3^{4+11}-9\cdot3^1^2}{46\cdot3^{18-4}}=\dfrac{8\cdot3^1^5-9\cdot3^1^2}{46\cdot3^1^4}=\dfrac{8\cdot3^3\cdot3^1^2-9\cdot3^1^2}{46\cdot3^1^4}=\\\\\\=\dfrac{(8\cdot3^3-9)\cdot3^1^2}{46\cdot3^1^4}=\dfrac{(8\cdot27-9)\cdot3^1^2}{46\cdot3^1^4}=\dfrac{(216-9)\cdot3^1^2}{46\cdot3^1^4}=\dfrac{\not207^9\cdot\not3^1^2}{\not46_{2}\cdot3^{14-12}}=\\\\\\=\dfrac{9}{2\cdot3^2}=\dfrac{9}{2\cdot9}=\dfrac{9}{18}=\dfrac{1}{2}[/tex]
Wykorzystano własności potęg
[tex]a^m\cdot a^n=a^{m+n}\\\\\frac{a^m}{a^n}=a^{m-n}[/tex]
