a)
3\sqrt3=3*3^{\frac{1}{2}}=3^{\frac{3}{2}}
b)
4^3*\sqrt[3]{4^2}=4^3*4^{\frac{2}{3}}=4^{3\frac{2}{3}}
c)
\sqrt{6^3}*\sqrt[3]{6^2}=6^{\frac{3}{2}}*6^{\frac{2}{3}}=6^{\frac{13}{6}}
Objaśnienie
\frac{3}{2}+\frac{2}{3}=\frac{9}{6}+\frac{4}{6}=\frac{13}{6}
d)
\sqrt{2\sqrt2}= (2\sqrt2)^{\frac{1}{2}}=2^{\frac{1}{2}}*(2^{\frac{1}{2}})^{\frac{1}{2}}=2^{\frac{1}{2}}*2^{\frac{1}{4}}=2^{\frac{3}{4}}
Lub
=\sqrt{2*2^{\frac{1}{2}}}=\sqrt{2^{\frac{3}{2}}}=(2^{\frac{3}{2}})^{\frac{1}{2}}=2^{\frac{3}{4}}
e)
\sqrt[3]{7*\sqrt[4]7}=\sqrt[3]{7*7^{\frac{1}{4}}}=\sqrt[3]{7^{\frac{5}{4}}}=(7^{\frac{5}{4}})^{\frac{1}{3}}=7^{\frac{5}{12}}
f)
\sqrt[3]{25*\sqrt5}=\sqrt[3]{5^2*5^{\frac{1}{2}}}=\sqrt[3]{5^{\frac{5}{2}}}=(5^{\frac{5}{2}})^{\frac{1}{3}}=5^{\frac{5}{6}}