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

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
2. \(\sqrt[4]{ (\frac{4}{9})^{2} }\)
3. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
4. \(\sqrt[4]{ (\frac{400}{9})^{2} }\)
5. \(\sqrt[3]{ (2)^{9} }\)
6. \(\sqrt[4]{ (\frac{20}{17})^{-8} }\)
7. \(\sqrt[4]{ (\frac{7}{10})^{8} }\)
8. \( \sqrt{ (\frac{3}{2})^{-8} } \)
9. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
10. \(\sqrt[4]{ (\frac{14}{19})^{8} }\)
11. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
12. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)

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

Verbetersleutel

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{-4}{16}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
2. \(\sqrt[4]{ (\frac{4}{9})^{2} }\\= (\frac{4}{9})^{\frac{-2}{4}}\\= (\frac{4}{9})^{\frac{-1}{2}}\\= \sqrt{ \frac{9}{4} } =\frac{3}{2}\)
3. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
4. \(\sqrt[4]{ (\frac{400}{9})^{2} }\\= (\frac{400}{9})^{\frac{2}{4}}\\= (\frac{400}{9})^{\frac{1}{2}}\\= \sqrt{ \frac{400}{9} } =\frac{20}{3}\)
5. \(\sqrt[3]{ (2)^{9} }\\= (2)^{\frac{9}{3}}\\= (2)^{3}=8\)
6. \(\sqrt[4]{ (\frac{20}{17})^{-8} }\\= (\frac{20}{17})^{\frac{-8}{4}}\\= (\frac{20}{17})^{-2}\\= (\frac{17}{20})^{2}= \frac{289}{400}\)
7. \(\sqrt[4]{ (\frac{7}{10})^{8} }\\= (\frac{7}{10})^{\frac{8}{4}}\\= (\frac{7}{10})^{2}=\frac{49}{100}\)
8. \( \sqrt{ (\frac{3}{2})^{-8} } \\= (\frac{3}{2})^{\frac{-8}{2}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
9. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{3}{9}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
10. \(\sqrt[4]{ (\frac{14}{19})^{8} }\\= (\frac{14}{19})^{\frac{8}{4}}\\= (\frac{14}{19})^{2}=\frac{196}{361}\)
11. \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
12. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{-4}{12}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)