a^{\frac{m}{n}}=(\sqrt[n]a)^m=\sqrt[n]{a^m}
a)
9^{\frac{3}{2}}=\sqrt{9^3}=\sqrt{(3^2)^3}=3^3=27
b)
3^{1\frac{2}{3}}=3^1*3^{\frac{2}{3}}=3*\sqrt[3]{3^2}=3\sqrt[3]9
c)
81^{-\frac{5}{4}}=(\frac{1}{81})^{\frac{5}{4}}=\frac{1}{(9^2)^{\frac{5}{4}}}=\frac{1}{9^{\frac{5}{2}}}=\frac{1}{\sqrt{9^5}}=\frac{1}{243}
d)
(0,5)^{-\frac{2}{3}}=(\frac{1}{2})^{-\frac{2}{3}}=2^{\frac{2}{3}}=\sqrt[3]{2^2}=\sqrt[3]{4}
e)(1/128) do potęgi 3/5
f)(2 \sqrt2)^{\frac{2}{3}}=\sqrt[3]{2^2}*\sqrt[3]{\sqrt{2^2}}=\sqrt[3]4*\sqrt[3]2=\sqrt[3]8=2
g)
0,625^{0,75}=(\frac{625}{1000})^{\frac{3}{4}}=(\frac{5}{8})^{\frac{3}{4}}=
h)
(5\frac{5}{24})^{-\frac{2}{3}}=(\frac{125}{24})^{-\frac{2}{3}}=(\frac{24}{125})^{\frac{2}{3}}=\sqrt[3]{(\frac{8*3}{5^3}})^2=\sqrt[3]{\frac{64*9}{25^3}}=\frac{4*\sqrt[3]9}{25}
i)
2^{-\frac{1}{2}}=(\frac{1}{2})^{\frac{1}{2}}=\frac{1}{2^{\frac{1}{2}}}=\frac{1}{\sqrt2}=\frac{\sqrt2}{\sqrt2*\sqrt2}=\frac{\sqrt2}{2}