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

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

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

Verbetersleutel

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