Odpowiedź:
[tex]a)\ \ 9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}=3^{2\cdot\frac{3}{2}}=3^3=27\\\\b)\ \ 125^{\frac{2}{3}}=(5^3)^{\frac{2}{3}}=5^{3\cdot\frac{2}{3}}=5^2=25\\\\c)\ \ 8^{-\frac{4}{3}}=(2^3)^{-\frac{4}{3}}=2^{3\cdot(-\frac{4}{3})}=2^{-4}=(\frac{1}{2})^4=\frac{1}{16}\\\\d)\ \ 27^{-\frac{2}{3}}=(3^3)^{-\frac{2}{3}}=3^{3\cdot(-\frac{2}{3})}=3^{-2}=(\frac{1}{3})^2=\frac{1}{9}\\\\e)\ \ 144^{-0,5}=144^{-\frac{1}{2}}=(12^2)^{-\frac{1}{2}}=12^{2\cdot(-\frac{1}{2})}=12^{-1}=\frac{1}{12}[/tex]
[tex]f)\ \ 16^{0,75}=16^{\frac{3}{4}}=(2^4)^{\frac{3}{4}}=2^{4\cdot\frac{3}{4}}=2^3=8\\\\g)\ \ 10000^{0,25}=10000^{\frac{1}{4}}=(10^4)^{\frac{1}{4}}=10^{4\cdot\frac{1}{4}}=10^1=10\\\\h)\ \ 81^{-0,125}=81^{-\frac{1}{8}}=(3^4)^{-\frac{1}{8}}=3^{4\cdot(-\frac{1}{8})}=3^{-\frac{1}{2}}=(\frac{1}{3})^{\frac{1}{2}}=\sqrt{\frac{1}{3}}=\frac{1}{\sqrt{3}}= \\\\=\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
