Zadanie 1
a)
\frac{2}{\sqrt3}=\frac{2}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}=\frac{2\sqrt3}{3}
b)
{\frac{3\sqrt3}{2\sqrt6}=\frac{3\sqrt3}{2\sqrt2\cdot \sqrt3}=\frac{3}{2\sqrt2}=\frac{3}{2\sqrt2}\cdot \frac{\sqrt2}{\sqrt2}=\frac{3\sqrt2}{2\cdot 2}=\frac{3\sqrt2}{4}}
c)
\frac{5}{\sqrt{45}}=\frac{5}{3\sqrt5}\cdot \frac{\sqrt5}{\sqrt5}=\frac{\not5^1\sqrt5}{3\cdot \not5^1}=\frac{\sqrt5}{3}
d)
\frac{2\sqrt7}{\sqrt3}=\frac{2\sqrt7}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}=\frac{2\sqrt{21}}{3}
Zadanie 2
a)
{\frac{9^{11}\cdot 3^{11}}{6^{11}\cdot 4^{11}}=\frac{27^{11}}{24^{11}}=(\frac{9}{8})^{11}=\frac{(3^2)^{11}}{(2^3)^{11}}=\frac{3^{22}}{2^{33}}}
b)
\frac{2^6\cdot 5^{-1}\cdot 2^{-4}\cdot 3^6}{3^{-2}}=2^2\cdot \frac{1}{5}\cdot 3^{6-(-2)}=\frac{4}{5}\cdot 3^8=0,8\cdot 3^8