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

1. \( \sqrt{ (\frac{4}{3})^{6} } \)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
3. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
4. \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
5. \( \sqrt{ (\frac{1}{2})^{6} } \)
6. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
7. \(\sqrt[8]{ (\frac{1}{4})^{4} }\)
8. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)
9. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
10. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
11. \(\sqrt[4]{ (\frac{15}{17})^{8} }\)
12. \(\sqrt[4]{ (\frac{4}{3})^{12} }\)

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

Verbetersleutel

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