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

1. \(\sqrt[4]{ (\frac{16}{17})^{-8} }\)
2. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
3. \(\sqrt[8]{ (\frac{25}{121})^{4} }\)
4. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
5. \(\sqrt[6]{ (\frac{49}{225})^{3} }\)
6. \( \sqrt{ (2)^{6} } \)
7. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
8. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
9. \( \sqrt{ (\frac{5}{3})^{4} } \)
10. \( \sqrt{ (\frac{17}{18})^{4} } \)
11. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)
12. \(\sqrt[3]{ (\frac{15}{17})^{-6} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{16}{17})^{-8} }\\= (\frac{16}{17})^{\frac{-8}{4}}\\= (\frac{16}{17})^{-2}\\= (\frac{17}{16})^{2}= \frac{289}{256}\)
2. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
3. \(\sqrt[8]{ (\frac{25}{121})^{4} }\\= (\frac{25}{121})^{\frac{4}{8}}\\= (\frac{25}{121})^{\frac{1}{2}}\\= \sqrt{ \frac{25}{121} } =\frac{5}{11}\)
4. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
5. \(\sqrt[6]{ (\frac{49}{225})^{3} }\\= (\frac{49}{225})^{\frac{3}{6}}\\= (\frac{49}{225})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{225} } =\frac{7}{15}\)
6. \( \sqrt{ (2)^{6} } \\= (2)^{\frac{6}{2}}\\= (2)^{3}=8\)
7. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
9. \( \sqrt{ (\frac{5}{3})^{4} } \\= (\frac{5}{3})^{\frac{4}{2}}\\= (\frac{5}{3})^{2}=\frac{25}{9}\)
10. \( \sqrt{ (\frac{17}{18})^{4} } \\= (\frac{17}{18})^{\frac{4}{2}}\\= (\frac{17}{18})^{2}=\frac{289}{324}\)
11. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{-4}{12}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
12. \(\sqrt[3]{ (\frac{15}{17})^{-6} }\\= (\frac{15}{17})^{\frac{-6}{3}}\\= (\frac{15}{17})^{-2}\\= (\frac{17}{15})^{2}= \frac{289}{225}\)