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

1. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
2. \(\sqrt[8]{ (\frac{64}{225})^{4} }\)
3. \( \sqrt{ (\frac{14}{19})^{-4} } \)
4. \(\sqrt[3]{ (\frac{3}{4})^{9} }\)
5. \( \sqrt{ (\frac{3}{2})^{8} } \)
6. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
7. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
8. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
9. \(\sqrt[3]{ (\frac{3}{4})^{6} }\)
10. \( \sqrt{ (\frac{8}{9})^{4} } \)
11. \(\sqrt[4]{ (\frac{289}{324})^{2} }\)
12. \( \sqrt{ (\frac{3}{4})^{6} } \)

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

Verbetersleutel

1. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{-3}{9}}\\= (\frac{8}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{8} }=\frac{3}{2}\)
2. \(\sqrt[8]{ (\frac{64}{225})^{4} }\\= (\frac{64}{225})^{\frac{4}{8}}\\= (\frac{64}{225})^{\frac{1}{2}}\\= \sqrt{ \frac{64}{225} } =\frac{8}{15}\)
3. \( \sqrt{ (\frac{14}{19})^{-4} } \\= (\frac{14}{19})^{\frac{-4}{2}}\\= (\frac{14}{19})^{-2}\\= (\frac{19}{14})^{2}= \frac{361}{196}\)
4. \(\sqrt[3]{ (\frac{3}{4})^{9} }\\= (\frac{3}{4})^{\frac{9}{3}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
5. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
6. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{-4}{12}}\\= (\frac{8}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{8} }=\frac{3}{2}\)
7. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
8. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
9. \(\sqrt[3]{ (\frac{3}{4})^{6} }\\= (\frac{3}{4})^{\frac{6}{3}}\\= (\frac{3}{4})^{2}=\frac{9}{16}\)
10. \( \sqrt{ (\frac{8}{9})^{4} } \\= (\frac{8}{9})^{\frac{4}{2}}\\= (\frac{8}{9})^{2}=\frac{64}{81}\)
11. \(\sqrt[4]{ (\frac{289}{324})^{2} }\\= (\frac{289}{324})^{\frac{2}{4}}\\= (\frac{289}{324})^{\frac{1}{2}}\\= \sqrt{ \frac{289}{324} } =\frac{17}{18}\)
12. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)