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

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
2. \(\sqrt[6]{ (\frac{1}{8})^{2} }\)
3. \( \sqrt{ (\frac{17}{18})^{4} } \)
4. \(\sqrt[4]{ (\frac{2}{7})^{8} }\)
5. \( \sqrt{ (\frac{9}{10})^{4} } \)
6. \(\sqrt[9]{ (\frac{64}{27})^{3} }\)
7. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
8. \( \sqrt{ (\frac{3}{4})^{6} } \)
9. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
10. \( \sqrt{ (\frac{2}{3})^{8} } \)
11. \(\sqrt[4]{ (\frac{81}{100})^{2} }\)
12. \(\sqrt[4]{ (\frac{25}{169})^{2} }\)

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

Verbetersleutel

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{-4}{16}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
2. \(\sqrt[6]{ (\frac{1}{8})^{2} }\\= (\frac{1}{8})^{\frac{-2}{6}}\\= (\frac{1}{8})^{\frac{-1}{3}}\\=\sqrt[3]{ 8 }=2\)
3. \( \sqrt{ (\frac{17}{18})^{4} } \\= (\frac{17}{18})^{\frac{4}{2}}\\= (\frac{17}{18})^{2}=\frac{289}{324}\)
4. \(\sqrt[4]{ (\frac{2}{7})^{8} }\\= (\frac{2}{7})^{\frac{8}{4}}\\= (\frac{2}{7})^{2}=\frac{4}{49}\)
5. \( \sqrt{ (\frac{9}{10})^{4} } \\= (\frac{9}{10})^{\frac{4}{2}}\\= (\frac{9}{10})^{2}=\frac{81}{100}\)
6. \(\sqrt[9]{ (\frac{64}{27})^{3} }\\= (\frac{64}{27})^{\frac{3}{9}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
7. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{3}{9}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
8. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
9. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{-4}{12}}\\= (\frac{8}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{8} }=\frac{3}{2}\)
10. \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
11. \(\sqrt[4]{ (\frac{81}{100})^{2} }\\= (\frac{81}{100})^{\frac{2}{4}}\\= (\frac{81}{100})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{100} } =\frac{9}{10}\)
12. \(\sqrt[4]{ (\frac{25}{169})^{2} }\\= (\frac{25}{169})^{\frac{2}{4}}\\= (\frac{25}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{25}{169} } =\frac{5}{13}\)