[latex]frac{9^{3}*3^{frac{3}{2}}}{sqrt{27}} =frac{(3^{2})^{3}*3^{frac{3}{2}}}{sqrt{3^{3}}} = \\=frac{3^{6}*3^{frac{3}{2}}}{3^{frac{3}{2}}} = 3^{6} = 729[/latex] LUB [latex]frac{9^{3}*3^{frac{3}{2}}}{sqrt{27}} = frac{9^{3}*sqrt{3^{3}}}{sqrt{27}} = \\= frac{9^{3}*sqrt{27}}{sqrt{27}} = 9^{3} = 729[/latex]
[latex] frac{9^3*3^{ frac{3}{2}}}{ sqrt{27}}= frac{(3^2)^3*3^ frac{3}{2}}{27^ frac{1}{2}}= frac{3^6*3^ frac{3}{2}}{(3^3)^ frac{1}{2}}= frac{3^6*3^ frac{3}{2}}{3^ frac{3}{2}}= frac{3^ frac{15}{2}}{3^ frac{3}{2}}=3^{ frac{15}{2}- frac{3}{2}}=3^6=729\ \ Korzystamy z:\ a^r*a^s=a^{r+s}\ (a^r)^s=a^{r*s}\ frac{a^r}{a^s}=a^{r-s}\ sqrt{a}=a^ frac{1}{2}\ Staramy sie zapisac wszystko o wspolnej podstawie jaka jest 3\ [/latex]
