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

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

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

Verbetersleutel

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