Zadanie 1
Oblicz.
a)
125^{\frac{1}{3}}=\sqrt[3]{5^3}=5^{\frac{3}{3}}=5^1=5
6^{-2}=(\frac{1}{6})^2=\frac{1}{36}
(\frac{3}{7})^{-1}=(\frac{7}{3})^1=\frac{7}{3}
(\frac{16}{81})^{\frac{1}{4}}=(\(\frac{2}{3})^4)^{\frac{1}{4}}=(\frac{2}{3})^{\frac{1}{4}*4}=(\frac{2}{3})^1=\frac{2}{3}
0,3^{-3}=(\frac{3}{10})^{-3}=(\frac{10}{3})^3=\frac{1000}{27}
1,21^{\frac{1}{2}}=\sqrt{1,21}=1,1
b)
4^{\frac{3}{2}}=(2^2)^{\frac{3}{2}}=2^{2*\frac{3}{2}}=2^3=8
32^{-\frac{1}{5}}=(2^5)^{-\frac{1}{5}}=2^{-1}=\frac{1}{2}
25^{-1,5}=(5^2)^{-\frac{3}{2}}=5^{-3}=(\frac{1}{5})^3=\frac{1}{125}
(\frac{64}{125})^{-\frac{2}{3}}=((\frac{4}{5})^3)^{-\frac{2}{3}}=(\frac{4}{5})^{-2}=(\frac{5}{4})^2=\frac{25}{16}
(0,0001)^{0,75}=(10^{-4})^{\frac{3}{4}}=10^{-3}=(\frac{1}{10})^3=\frac{1}{1000}
(0,027)^{-\frac{4}{3}}=(0,3^3)^{-\frac{4}{3}}=(0,3)^{-4}=(\frac{3}{10})^{-4}=(\frac{10}{3})^4=\frac{10000}{81}