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

1. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
2. \(\sqrt[3]{ (\frac{7}{10})^{6} }\)
3. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
4. \(\sqrt[8]{ (\frac{324}{361})^{4} }\)
5. \( \sqrt{ (\frac{3}{4})^{6} } \)
6. \(\sqrt[3]{ (\frac{5}{12})^{-6} }\)
7. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
8. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\)
9. \(\sqrt[4]{ (\frac{1}{25})^{2} }\)
10. \(\sqrt[6]{ (\frac{1}{8})^{2} }\)
11. \(\sqrt[4]{ (\frac{25}{256})^{2} }\)
12. \(\sqrt[4]{ (\frac{19}{20})^{-8} }\)

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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. \(\sqrt[3]{ (\frac{7}{10})^{6} }\\= (\frac{7}{10})^{\frac{6}{3}}\\= (\frac{7}{10})^{2}=\frac{49}{100}\)
3. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{-2}{8}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
4. \(\sqrt[8]{ (\frac{324}{361})^{4} }\\= (\frac{324}{361})^{\frac{4}{8}}\\= (\frac{324}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{324}{361} } =\frac{18}{19}\)
5. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
6. \(\sqrt[3]{ (\frac{5}{12})^{-6} }\\= (\frac{5}{12})^{\frac{-6}{3}}\\= (\frac{5}{12})^{-2}\\= (\frac{12}{5})^{2}= \frac{144}{25}\)
7. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\\= (\frac{3}{2})^{\frac{-16}{4}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
9. \(\sqrt[4]{ (\frac{1}{25})^{2} }\\= (\frac{1}{25})^{\frac{2}{4}}\\= (\frac{1}{25})^{\frac{1}{2}}\\= \sqrt{ \frac{1}{25} } =\frac{1}{5}\)
10. \(\sqrt[6]{ (\frac{1}{8})^{2} }\\= (\frac{1}{8})^{\frac{-2}{6}}\\= (\frac{1}{8})^{\frac{-1}{3}}\\=\sqrt[3]{ 8 }=2\)
11. \(\sqrt[4]{ (\frac{25}{256})^{2} }\\= (\frac{25}{256})^{\frac{-2}{4}}\\= (\frac{25}{256})^{\frac{-1}{2}}\\= \sqrt{ \frac{256}{25} } =\frac{16}{5}\)
12. \(\sqrt[4]{ (\frac{19}{20})^{-8} }\\= (\frac{19}{20})^{\frac{-8}{4}}\\= (\frac{19}{20})^{-2}\\= (\frac{20}{19})^{2}= \frac{400}{361}\)