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

1. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
2. \(\sqrt[4]{ (\frac{81}{361})^{2} }\)
3. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
4. \(\sqrt[4]{ (\frac{7}{10})^{8} }\)
5. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
6. \(\sqrt[6]{ (\frac{49}{100})^{3} }\)
7. \( \sqrt{ (\frac{2}{3})^{6} } \)
8. \( \sqrt{ (\frac{20}{17})^{4} } \)
9. \( \sqrt{ (\frac{1}{2})^{-6} } \)
10. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
11. \( \sqrt{ (\frac{2}{3})^{8} } \)
12. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
2. \(\sqrt[4]{ (\frac{81}{361})^{2} }\\= (\frac{81}{361})^{\frac{2}{4}}\\= (\frac{81}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{361} } =\frac{9}{19}\)
3. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
4. \(\sqrt[4]{ (\frac{7}{10})^{8} }\\= (\frac{7}{10})^{\frac{8}{4}}\\= (\frac{7}{10})^{2}=\frac{49}{100}\)
5. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
6. \(\sqrt[6]{ (\frac{49}{100})^{3} }\\= (\frac{49}{100})^{\frac{3}{6}}\\= (\frac{49}{100})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{100} } =\frac{7}{10}\)
7. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
8. \( \sqrt{ (\frac{20}{17})^{4} } \\= (\frac{20}{17})^{\frac{4}{2}}\\= (\frac{20}{17})^{2}=\frac{400}{289}\)
9. \( \sqrt{ (\frac{1}{2})^{-6} } \\= (\frac{1}{2})^{\frac{-6}{2}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
10. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
11. \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
12. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\\= (\frac{2}{3})^{\frac{-16}{4}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)