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

1. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
2. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)
3. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
4. \( \sqrt{ (\frac{7}{10})^{4} } \)
5. \( \sqrt{ (\frac{15}{16})^{-4} } \)
6. \(\sqrt[3]{ (\frac{3}{19})^{6} }\)
7. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\)
8. \(\sqrt[3]{ (\frac{3}{4})^{9} }\)
9. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\)
10. \(\sqrt[3]{ (\frac{11}{15})^{6} }\)
11. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
12. \(\sqrt[9]{ (8)^{3} }\)

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
2. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
3. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
4. \( \sqrt{ (\frac{7}{10})^{4} } \\= (\frac{7}{10})^{\frac{4}{2}}\\= (\frac{7}{10})^{2}=\frac{49}{100}\)
5. \( \sqrt{ (\frac{15}{16})^{-4} } \\= (\frac{15}{16})^{\frac{-4}{2}}\\= (\frac{15}{16})^{-2}\\= (\frac{16}{15})^{2}= \frac{256}{225}\)
6. \(\sqrt[3]{ (\frac{3}{19})^{6} }\\= (\frac{3}{19})^{\frac{6}{3}}\\= (\frac{3}{19})^{2}=\frac{9}{361}\)
7. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\\= (\frac{3}{4})^{\frac{-9}{3}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
8. \(\sqrt[3]{ (\frac{3}{4})^{9} }\\= (\frac{3}{4})^{\frac{9}{3}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
9. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\\= (\frac{2}{3})^{\frac{-16}{4}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
10. \(\sqrt[3]{ (\frac{11}{15})^{6} }\\= (\frac{11}{15})^{\frac{6}{3}}\\= (\frac{11}{15})^{2}=\frac{121}{225}\)
11. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
12. \(\sqrt[9]{ (8)^{3} }\\= (8)^{\frac{3}{9}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)