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

1. \(\sqrt[6]{ (\frac{9}{169})^{3} }\)
2. \(\sqrt[6]{ (8)^{2} }\)
3. \( \sqrt{ (\frac{3}{4})^{6} } \)
4. \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
5. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
6. \(\sqrt[4]{ (\frac{3}{4})^{-8} }\)
7. \(\sqrt[4]{ (\frac{2}{3})^{12} }\)
8. \(\sqrt[6]{ (\frac{25}{121})^{3} }\)
9. \(\sqrt[8]{ (\frac{400}{121})^{4} }\)
10. \( \sqrt{ (\frac{6}{7})^{-4} } \)
11. \(\sqrt[8]{ (\frac{324}{361})^{4} }\)
12. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)

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

Verbetersleutel

1. \(\sqrt[6]{ (\frac{9}{169})^{3} }\\= (\frac{9}{169})^{\frac{3}{6}}\\= (\frac{9}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{9}{169} } =\frac{3}{13}\)
2. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
3. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
4. \(\sqrt[9]{ (\frac{27}{64})^{3} }\\= (\frac{27}{64})^{\frac{3}{9}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
5. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
6. \(\sqrt[4]{ (\frac{3}{4})^{-8} }\\= (\frac{3}{4})^{\frac{-8}{4}}\\= (\frac{3}{4})^{-2}\\= (\frac{4}{3})^{2}= \frac{16}{9}\)
7. \(\sqrt[4]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{4}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
8. \(\sqrt[6]{ (\frac{25}{121})^{3} }\\= (\frac{25}{121})^{\frac{3}{6}}\\= (\frac{25}{121})^{\frac{1}{2}}\\= \sqrt{ \frac{25}{121} } =\frac{5}{11}\)
9. \(\sqrt[8]{ (\frac{400}{121})^{4} }\\= (\frac{400}{121})^{\frac{-4}{8}}\\= (\frac{400}{121})^{\frac{-1}{2}}\\= \sqrt{ \frac{121}{400} } =\frac{11}{20}\)
10. \( \sqrt{ (\frac{6}{7})^{-4} } \\= (\frac{6}{7})^{\frac{-4}{2}}\\= (\frac{6}{7})^{-2}\\= (\frac{7}{6})^{2}= \frac{49}{36}\)
11. \(\sqrt[8]{ (\frac{324}{361})^{4} }\\= (\frac{324}{361})^{\frac{4}{8}}\\= (\frac{324}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{324}{361} } =\frac{18}{19}\)
12. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)