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

1. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\)
2. \(\sqrt[3]{ (\frac{16}{17})^{-6} }\)
3. \(\sqrt[8]{ (\frac{400}{169})^{4} }\)
4. \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
5. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
6. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
8. \(\sqrt[4]{ (\frac{16}{17})^{8} }\)
9. \(\sqrt[6]{ (\frac{256}{289})^{3} }\)
10. \(\sqrt[4]{ (\frac{4}{3})^{12} }\)
11. \(\sqrt[8]{ (\frac{36}{361})^{4} }\)
12. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\\= (\frac{3}{4})^{\frac{-12}{4}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
2. \(\sqrt[3]{ (\frac{16}{17})^{-6} }\\= (\frac{16}{17})^{\frac{-6}{3}}\\= (\frac{16}{17})^{-2}\\= (\frac{17}{16})^{2}= \frac{289}{256}\)
3. \(\sqrt[8]{ (\frac{400}{169})^{4} }\\= (\frac{400}{169})^{\frac{4}{8}}\\= (\frac{400}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{400}{169} } =\frac{20}{13}\)
4. \(\sqrt[9]{ (\frac{27}{64})^{3} }\\= (\frac{27}{64})^{\frac{3}{9}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
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. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{-2}{8}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \(\sqrt[4]{ (\frac{16}{17})^{8} }\\= (\frac{16}{17})^{\frac{8}{4}}\\= (\frac{16}{17})^{2}=\frac{256}{289}\)
9. \(\sqrt[6]{ (\frac{256}{289})^{3} }\\= (\frac{256}{289})^{\frac{3}{6}}\\= (\frac{256}{289})^{\frac{1}{2}}\\= \sqrt{ \frac{256}{289} } =\frac{16}{17}\)
10. \(\sqrt[4]{ (\frac{4}{3})^{12} }\\= (\frac{4}{3})^{\frac{12}{4}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
11. \(\sqrt[8]{ (\frac{36}{361})^{4} }\\= (\frac{36}{361})^{\frac{-4}{8}}\\= (\frac{36}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{36} } =\frac{19}{6}\)
12. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)