Zadanie 5.3
a)
8^{\frac{2}{3}}=(2^3)^{\frac{2}{3}}=2^{3*\frac{2}{3}}=2^2=4
9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}=3^{2*\frac{3}{2}}=3^3=27
27^{\frac{4}{3}}=(3^3)^{\frac{4}{3}}=3^4=81
16^{\frac{3}{4}}=(2^4)^{\frac{3}{4}}=2^3=8
64^{\frac{1}{6}}=(2^6)^{\frac{1}{6}}=2
81^{\frac{5}{4}}=(3^4)^{\frac{5}{4}}=3^5=243
125^{\frac{5}{3}}=(5^3)^{\frac{5}{3}}=5^5=3125
32^{\frac{7}{5}}=(2^5)^{\frac{7}{5}}=2^7=128
b)
1000^{\frac{4}{3}}=(10^3)^{\frac{4}{3}}=10^4=10000
1000000^{\frac{5}{6}}=(10^6)^{\frac{5}{6}}=10^5=100000
36^{0,5}=(6^2)^{0,5}=6^{2*0,5}=6^1=6
32^{0,2}=(2^5)^{0,2}=2^{5*0,2}=5^1=5
16^{-\frac{1}{2}}=(\frac{1}{16})^{\frac{1}{2}}=\sqrt{\frac{1}{16}}=\frac{1}{4}
81^{-\frac{3}{4}}=(3^4)^{-\frac{3}{4}}=3^{-3}=(\frac{1}{3})^3=\frac{1}{27}
64^{-\frac{2}{3}}=(2^6)^{-\frac{2}{3}}=2^{-\frac{12}{3}}=2^{-4}=(\frac{1}{2})^4=\frac{1}{16}
c)
64^{-\frac{5}{6}}=(2^6)^{-\frac{5}{6}}=5^{-5}=(\frac{1}{2})^5=\frac{1}{32}
(\frac{1}{4})^{-\frac{1}{2}}=4^{\frac{1}{2}}=\sqrt4=2
(2\frac{1}{4})^{-\frac{3}{2}}=(\frac{9}{4})^{-\frac{3}{2}}=(\frac{4}{9})^{\frac{3}{2}}=((\frac{2}{3})^2)^{\frac{3}{2}}=(\frac{2}{3})^3=\frac{8}{27}
(3\frac{3}{8})^{-\frac{1}{3}}=(\frac{27}{8})^{-\frac{1}{3}}=(\frac{8}{27})^{\frac{1}{3}}=((\frac{2}{3})^3)^{\frac{1}{3}}=\frac{2}{3}
0,008^{-\frac{2}{3}}=((0,2)^3)^{-\frac{2}{3}}=0,2^{-2}=(\frac{2}{10})^{-2}=(\frac{1}{5})^2=\frac{1}{25}