Question

80. Oblicz. (pls daje naj)


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Answer 1

[tex]4^{\frac{1}{2}}=\sqrt{4}=2\\\\\\8^{-\frac{1}{3}}=\frac{1}{\sqrt[3]{8}}=\frac{1}{2}\\\\\\27^{\frac{2}{3}}=(\sqrt[3]{27})^2=3^2=9\\\\\\32^{1,6}=32^{\frac{16}{10}}=32^{\frac{8}{5}}=(2^5)^{\frac{8}{5}}=2^{\not5\cdot\frac{8}{\not5}}= 2^8=256\\\\\\81^{-1,25}=81^{-\frac{125}{100}}=81^{-\frac{5}{4}}=(3^4)^{-\frac{5}{4}}=3^{-\frac{20}{4}}=3^{-5}=(\frac{1}{3})^5=\frac{1}{243}\\\\\\9^{2,5}=(3^2)^{2,5}=3^5=243[/tex]

[tex]0,01^{-1,5}=(\frac{1}{100})^{-\frac{15}{10}}=(\frac{1}{100})^{-\frac{3}{2}}=100^{\frac{3}{2}}=(10^2)^{\frac{3}{2}}=10^{\not2\cdot\frac{3}{\not2}}=10^3=1000\\\\\\0,0016^{0,75}=(\frac{16}{10000})^{0,75}=(\frac{1}{625})^{0,75}=((\frac{1}{5})^4)^{0,75}=(5^{-4})^{0,75}=5^{-3}=\\\\=(\frac{1}{5})^3=\frac{1}{125}[/tex]

[tex](3\frac{3}{8})^{\frac{4}{3}}=(\frac{27}{8})^{\frac{4}{3}}=\left(\sqrt[3]{\frac{27}{8}}\right)^4=(\frac{3}{2})^4=\frac{81}{16}=5\frac{1}{16}\\\\\\(5\frac{1}{16})^{-1\frac{1}{4}}=(\frac{81}{16})^{-\frac{5}{4}}=(\frac{16}{81}})^{\frac{5}{4}}=\left(\sqrt[4]{\frac{16}{81}}\right)^5=(\frac{2}{3})^5=\frac{32}{243}[/tex]

[tex]100000^{-0,4}=(10^5)^{-0,4}=10^{-2}=(\frac{1}{10})^2=\frac{1}{100}\\\\\\a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]