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

1. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
2. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
3. \(\sqrt[9]{ (\frac{64}{27})^{3} }\)
4. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
5. \(\sqrt[4]{ (\frac{100}{361})^{2} }\)
6. \( \sqrt{ (\frac{13}{16})^{4} } \)
7. \(\sqrt[4]{ (\frac{13}{20})^{-8} }\)
8. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\)
9. \( \sqrt{ (\frac{3}{4})^{6} } \)
10. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
11. \(\sqrt[4]{ (\frac{1}{2})^{12} }\)
12. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)

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

Verbetersleutel

1. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{2}{8}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
2. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{-4}{16}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
3. \(\sqrt[9]{ (\frac{64}{27})^{3} }\\= (\frac{64}{27})^{\frac{3}{9}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
4. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{-3}{12}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
5. \(\sqrt[4]{ (\frac{100}{361})^{2} }\\= (\frac{100}{361})^{\frac{-2}{4}}\\= (\frac{100}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{100} } =\frac{19}{10}\)
6. \( \sqrt{ (\frac{13}{16})^{4} } \\= (\frac{13}{16})^{\frac{4}{2}}\\= (\frac{13}{16})^{2}=\frac{169}{256}\)
7. \(\sqrt[4]{ (\frac{13}{20})^{-8} }\\= (\frac{13}{20})^{\frac{-8}{4}}\\= (\frac{13}{20})^{-2}\\= (\frac{20}{13})^{2}= \frac{400}{169}\)
8. \(\sqrt[4]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{4}}\\= (\frac{2}{3})^{-3}\\= (\frac{3}{2})^{3}= \frac{27}{8}\)
9. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
10. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
11. \(\sqrt[4]{ (\frac{1}{2})^{12} }\\= (\frac{1}{2})^{\frac{12}{4}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
12. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{3}{9}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)