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

1. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
2. \(\sqrt[4]{ (\frac{20}{11})^{8} }\)
3. \(\sqrt[4]{ (\frac{9}{10})^{-8} }\)
4. \(\sqrt[4]{ (\frac{16}{361})^{2} }\)
5. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
6. \(\sqrt[4]{ (\frac{81}{100})^{2} }\)
7. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
8. \(\sqrt[4]{ (\frac{256}{289})^{2} }\)
9. \( \sqrt{ (\frac{4}{3})^{6} } \)
10. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
11. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
12. \(\sqrt[3]{ (\frac{10}{11})^{6} }\)

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

Verbetersleutel

1. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
2. \(\sqrt[4]{ (\frac{20}{11})^{8} }\\= (\frac{20}{11})^{\frac{8}{4}}\\= (\frac{20}{11})^{2}=\frac{400}{121}\)
3. \(\sqrt[4]{ (\frac{9}{10})^{-8} }\\= (\frac{9}{10})^{\frac{-8}{4}}\\= (\frac{9}{10})^{-2}\\= (\frac{10}{9})^{2}= \frac{100}{81}\)
4. \(\sqrt[4]{ (\frac{16}{361})^{2} }\\= (\frac{16}{361})^{\frac{-2}{4}}\\= (\frac{16}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{16} } =\frac{19}{4}\)
5. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{-2}{8}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
6. \(\sqrt[4]{ (\frac{81}{100})^{2} }\\= (\frac{81}{100})^{\frac{-2}{4}}\\= (\frac{81}{100})^{\frac{-1}{2}}\\= \sqrt{ \frac{100}{81} } =\frac{10}{9}\)
7. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
8. \(\sqrt[4]{ (\frac{256}{289})^{2} }\\= (\frac{256}{289})^{\frac{-2}{4}}\\= (\frac{256}{289})^{\frac{-1}{2}}\\= \sqrt{ \frac{289}{256} } =\frac{17}{16}\)
9. \( \sqrt{ (\frac{4}{3})^{6} } \\= (\frac{4}{3})^{\frac{6}{2}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
10. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
11. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{3}{9}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
12. \(\sqrt[3]{ (\frac{10}{11})^{6} }\\= (\frac{10}{11})^{\frac{6}{3}}\\= (\frac{10}{11})^{2}=\frac{100}{121}\)