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

1. \(\sqrt[8]{ (\frac{49}{100})^{4} }\)
2. \(\sqrt[4]{ (\frac{121}{169})^{2} }\)
3. \(\sqrt[6]{ (\frac{25}{36})^{3} }\)
4. \(\sqrt[6]{ (8)^{2} }\)
5. \(\sqrt[6]{ (\frac{1}{8})^{2} }\)
6. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
7. \(\sqrt[4]{ (\frac{1}{6})^{8} }\)
8. \(\sqrt[6]{ (\frac{361}{400})^{3} }\)
9. \( \sqrt{ (\frac{2}{3})^{-8} } \)
10. \(\sqrt[9]{ (\frac{1}{8})^{3} }\)
11. \(\sqrt[3]{ (\frac{17}{18})^{6} }\)
12. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)

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

Verbetersleutel

1. \(\sqrt[8]{ (\frac{49}{100})^{4} }\\= (\frac{49}{100})^{\frac{-4}{8}}\\= (\frac{49}{100})^{\frac{-1}{2}}\\= \sqrt{ \frac{100}{49} } =\frac{10}{7}\)
2. \(\sqrt[4]{ (\frac{121}{169})^{2} }\\= (\frac{121}{169})^{\frac{2}{4}}\\= (\frac{121}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{121}{169} } =\frac{11}{13}\)
3. \(\sqrt[6]{ (\frac{25}{36})^{3} }\\= (\frac{25}{36})^{\frac{3}{6}}\\= (\frac{25}{36})^{\frac{1}{2}}\\= \sqrt{ \frac{25}{36} } =\frac{5}{6}\)
4. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{-2}{6}}\\= (8)^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
5. \(\sqrt[6]{ (\frac{1}{8})^{2} }\\= (\frac{1}{8})^{\frac{2}{6}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
6. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
7. \(\sqrt[4]{ (\frac{1}{6})^{8} }\\= (\frac{1}{6})^{\frac{8}{4}}\\= (\frac{1}{6})^{2}=\frac{1}{36}\)
8. \(\sqrt[6]{ (\frac{361}{400})^{3} }\\= (\frac{361}{400})^{\frac{-3}{6}}\\= (\frac{361}{400})^{\frac{-1}{2}}\\= \sqrt{ \frac{400}{361} } =\frac{20}{19}\)
9. \( \sqrt{ (\frac{2}{3})^{-8} } \\= (\frac{2}{3})^{\frac{-8}{2}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
10. \(\sqrt[9]{ (\frac{1}{8})^{3} }\\= (\frac{1}{8})^{\frac{3}{9}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
11. \(\sqrt[3]{ (\frac{17}{18})^{6} }\\= (\frac{17}{18})^{\frac{6}{3}}\\= (\frac{17}{18})^{2}=\frac{289}{324}\)
12. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)