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

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

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{289}{324})^{2} }\\= (\frac{289}{324})^{\frac{-2}{4}}\\= (\frac{289}{324})^{\frac{-1}{2}}\\= \sqrt{ \frac{324}{289} } =\frac{18}{17}\)
2. \(\sqrt[6]{ (\frac{81}{100})^{3} }\\= (\frac{81}{100})^{\frac{3}{6}}\\= (\frac{81}{100})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{100} } =\frac{9}{10}\)
3. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
4. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{2}{8}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
5. \(\sqrt[8]{ (\frac{49}{64})^{4} }\\= (\frac{49}{64})^{\frac{-4}{8}}\\= (\frac{49}{64})^{\frac{-1}{2}}\\= \sqrt{ \frac{64}{49} } =\frac{8}{7}\)
6. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
7. \(\sqrt[8]{ (\frac{49}{64})^{4} }\\= (\frac{49}{64})^{\frac{-4}{8}}\\= (\frac{49}{64})^{\frac{-1}{2}}\\= \sqrt{ \frac{64}{49} } =\frac{8}{7}\)
8. \( \sqrt{ (\frac{5}{9})^{4} } \\= (\frac{5}{9})^{\frac{4}{2}}\\= (\frac{5}{9})^{2}=\frac{25}{81}\)
9. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
10. \( \sqrt{ (\frac{11}{18})^{4} } \\= (\frac{11}{18})^{\frac{4}{2}}\\= (\frac{11}{18})^{2}=\frac{121}{324}\)
11. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
12. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)