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

  1. \( \sqrt{ (\frac{2}{3})^{-8} } \)
  2. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
  3. \(\sqrt[8]{ (\frac{9}{64})^{4} }\)
  4. \(\sqrt[3]{ (\frac{4}{3})^{9} }\)
  5. \(\sqrt[4]{ (2)^{12} }\)
  6. \(\sqrt[4]{ (\frac{2}{3})^{12} }\)
  7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
  8. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
  9. \(\sqrt[4]{ (\frac{20}{11})^{8} }\)
  10. \(\sqrt[4]{ (\frac{256}{361})^{2} }\)
  11. \(\sqrt[4]{ (2)^{-12} }\)
  12. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\)

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

Verbetersleutel

  1. \( \sqrt{ (\frac{2}{3})^{-8} } \\= (\frac{2}{3})^{\frac{-8}{2}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
  2. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{2}{8}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
  3. \(\sqrt[8]{ (\frac{9}{64})^{4} }\\= (\frac{9}{64})^{\frac{4}{8}}\\= (\frac{9}{64})^{\frac{1}{2}}\\= \sqrt{ \frac{9}{64} } =\frac{3}{8}\)
  4. \(\sqrt[3]{ (\frac{4}{3})^{9} }\\= (\frac{4}{3})^{\frac{9}{3}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
  5. \(\sqrt[4]{ (2)^{12} }\\= (2)^{\frac{12}{4}}\\= (2)^{3}=8\)
  6. \(\sqrt[4]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{4}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
  7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
  8. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
  9. \(\sqrt[4]{ (\frac{20}{11})^{8} }\\= (\frac{20}{11})^{\frac{8}{4}}\\= (\frac{20}{11})^{2}=\frac{400}{121}\)
  10. \(\sqrt[4]{ (\frac{256}{361})^{2} }\\= (\frac{256}{361})^{\frac{-2}{4}}\\= (\frac{256}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{256} } =\frac{19}{16}\)
  11. \(\sqrt[4]{ (2)^{-12} }\\= (2)^{\frac{-12}{4}}\\= (2)^{-3}\\= (\frac{1}{2})^{3}= \frac{1}{8}\)
  12. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{4}}\\= (\frac{2}{3})^{-3}\\= (\frac{3}{2})^{3}= \frac{27}{8}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 08:22:24