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

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

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