Zadanie 4
a)
8\sqrt2=2^3\cdot 2^{\frac{1}{2}}=2^{3,5}
b)
4\sqrt[3]{2}=2^2\cdot 2^{\frac{1}{3}}=2^{\frac{6}{3}+\frac{1}{3}}=2^{\frac{7}{3}}
c)
\frac{\sqrt{27}}{9}=\frac{\sqrt{3^2\cdot 3}}{3\cdot 3}=\frac{\not3^1\sqrt3}{\not3^1\cdot 3}=\frac{\sqrt3}{3}
d)
\sqrt[4]{3\sqrt3}=3^{\frac{1}{4}}\cdot ((3^{\frac{1}{2}})^{\frac{1}{4}}=3^{\frac{2}{8}+\frac{1}{8}}=3^{\frac{3}{8}}
e)
$\sqrt{5\sqrt{5\sqrt5}}=5^{\frac{1}{2}}\cdot (5^{\frac{1}{2}})^{\frac{1}{2}}\cdot ((5^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}=$$5^{\frac{1}{2}}\cdot 5^{\frac{1}{4}}\cdot 5^{\frac{1}{8}}=5^{\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}=5^{\frac{7}{8}}
f)
{\sqrt[3]{16}\cdot \sqrt{2\cdot \sqrt[4]{8}}=(2^4)^{\frac{1}{3}}\cdot 2^{\frac{1}{2}}\cdot ((2^3)^{\frac{1}{4}})^{\frac{1}{2}}=2^{\frac{4}{3}}\cdot 2^{\frac{1}{2}}\cdot 2^{\frac{3}{8}}=2^{\frac{32+12+9}{24}}=2^{\frac{53}{24}}}$