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Bereken m.b.v. de rekenregels (zonder ZRM)

  1. \( \sqrt{ (\frac{3}{2})^{8} } \)
  2. \(\sqrt[3]{ (\frac{5}{4})^{6} }\)
  3. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
  4. \(\sqrt[4]{ (\frac{49}{81})^{2} }\)
  5. \(\sqrt[6]{ (8)^{2} }\)
  6. \(\sqrt[4]{ (\frac{4}{3})^{12} }\)
  7. \(\sqrt[6]{ (\frac{1}{9})^{3} }\)
  8. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\)
  9. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
  10. \(\sqrt[6]{ (\frac{196}{361})^{3} }\)
  11. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
  12. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)

Bereken m.b.v. de rekenregels (zonder ZRM)

Verbetersleutel

  1. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
  2. \(\sqrt[3]{ (\frac{5}{4})^{6} }\\= (\frac{5}{4})^{\frac{6}{3}}\\= (\frac{5}{4})^{2}=\frac{25}{16}\)
  3. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
  4. \(\sqrt[4]{ (\frac{49}{81})^{2} }\\= (\frac{49}{81})^{\frac{2}{4}}\\= (\frac{49}{81})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{81} } =\frac{7}{9}\)
  5. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{-2}{6}}\\= (8)^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
  6. \(\sqrt[4]{ (\frac{4}{3})^{12} }\\= (\frac{4}{3})^{\frac{12}{4}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
  7. \(\sqrt[6]{ (\frac{1}{9})^{3} }\\= (\frac{1}{9})^{\frac{3}{6}}\\= (\frac{1}{9})^{\frac{1}{2}}\\= \sqrt{ \frac{1}{9} } =\frac{1}{3}\)
  8. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{4}}\\= (\frac{2}{3})^{-3}\\= (\frac{3}{2})^{3}= \frac{27}{8}\)
  9. \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
  10. \(\sqrt[6]{ (\frac{196}{361})^{3} }\\= (\frac{196}{361})^{\frac{-3}{6}}\\= (\frac{196}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{196} } =\frac{19}{14}\)
  11. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
  12. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{-4}{12}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:28:01