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

1. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
2. \(\sqrt[4]{ (\frac{100}{9})^{2} }\)
3. \( \sqrt{ (\frac{2}{3})^{6} } \)
4. \(\sqrt[3]{ (\frac{14}{15})^{6} }\)
5. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\)
6. \(\sqrt[4]{ (\frac{25}{81})^{2} }\)
7. \(\sqrt[8]{ (\frac{81}{100})^{4} }\)
8. \(\sqrt[6]{ (\frac{1}{8})^{2} }\)
9. \(\sqrt[3]{ (\frac{15}{17})^{6} }\)
10. \( \sqrt{ (\frac{2}{3})^{8} } \)
11. \(\sqrt[8]{ (\frac{225}{361})^{4} }\)
12. \(\sqrt[3]{ (\frac{17}{18})^{-6} }\)

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
2. \(\sqrt[4]{ (\frac{100}{9})^{2} }\\= (\frac{100}{9})^{\frac{2}{4}}\\= (\frac{100}{9})^{\frac{1}{2}}\\= \sqrt{ \frac{100}{9} } =\frac{10}{3}\)
3. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
4. \(\sqrt[3]{ (\frac{14}{15})^{6} }\\= (\frac{14}{15})^{\frac{6}{3}}\\= (\frac{14}{15})^{2}=\frac{196}{225}\)
5. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\\= (\frac{3}{4})^{\frac{-12}{4}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
6. \(\sqrt[4]{ (\frac{25}{81})^{2} }\\= (\frac{25}{81})^{\frac{2}{4}}\\= (\frac{25}{81})^{\frac{1}{2}}\\= \sqrt{ \frac{25}{81} } =\frac{5}{9}\)
7. \(\sqrt[8]{ (\frac{81}{100})^{4} }\\= (\frac{81}{100})^{\frac{-4}{8}}\\= (\frac{81}{100})^{\frac{-1}{2}}\\= \sqrt{ \frac{100}{81} } =\frac{10}{9}\)
8. \(\sqrt[6]{ (\frac{1}{8})^{2} }\\= (\frac{1}{8})^{\frac{2}{6}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
9. \(\sqrt[3]{ (\frac{15}{17})^{6} }\\= (\frac{15}{17})^{\frac{6}{3}}\\= (\frac{15}{17})^{2}=\frac{225}{289}\)
10. \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
11. \(\sqrt[8]{ (\frac{225}{361})^{4} }\\= (\frac{225}{361})^{\frac{4}{8}}\\= (\frac{225}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{225}{361} } =\frac{15}{19}\)
12. \(\sqrt[3]{ (\frac{17}{18})^{-6} }\\= (\frac{17}{18})^{\frac{-6}{3}}\\= (\frac{17}{18})^{-2}\\= (\frac{18}{17})^{2}= \frac{324}{289}\)