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

1. \(\sqrt[6]{ (8)^{2} }\)
2. \(\sqrt[6]{ (\frac{64}{27})^{2} }\)
3. \(\sqrt[4]{ (\frac{169}{196})^{2} }\)
4. \(\sqrt[12]{ (\frac{27}{64})^{4} }\)
5. \(\sqrt[4]{ (\frac{3}{4})^{8} }\)
6. \( \sqrt{ (\frac{18}{19})^{4} } \)
7. \( \sqrt{ (2)^{-6} } \)
8. \(\sqrt[4]{ (\frac{4}{17})^{-8} }\)
9. \( \sqrt{ (\frac{2}{3})^{8} } \)
10. \(\sqrt[4]{ (\frac{2}{3})^{8} }\)
11. \(\sqrt[4]{ (\frac{19}{20})^{8} }\)
12. \( \sqrt{ (\frac{3}{2})^{8} } \)

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

Verbetersleutel

1. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
2. \(\sqrt[6]{ (\frac{64}{27})^{2} }\\= (\frac{64}{27})^{\frac{2}{6}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
3. \(\sqrt[4]{ (\frac{169}{196})^{2} }\\= (\frac{169}{196})^{\frac{-2}{4}}\\= (\frac{169}{196})^{\frac{-1}{2}}\\= \sqrt{ \frac{196}{169} } =\frac{14}{13}\)
4. \(\sqrt[12]{ (\frac{27}{64})^{4} }\\= (\frac{27}{64})^{\frac{4}{12}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
5. \(\sqrt[4]{ (\frac{3}{4})^{8} }\\= (\frac{3}{4})^{\frac{8}{4}}\\= (\frac{3}{4})^{2}=\frac{9}{16}\)
6. \( \sqrt{ (\frac{18}{19})^{4} } \\= (\frac{18}{19})^{\frac{4}{2}}\\= (\frac{18}{19})^{2}=\frac{324}{361}\)
7. \( \sqrt{ (2)^{-6} } \\= (2)^{\frac{-6}{2}}\\= (2)^{-3}\\= (\frac{1}{2})^{3}= \frac{1}{8}\)
8. \(\sqrt[4]{ (\frac{4}{17})^{-8} }\\= (\frac{4}{17})^{\frac{-8}{4}}\\= (\frac{4}{17})^{-2}\\= (\frac{17}{4})^{2}= \frac{289}{16}\)
9. \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
10. \(\sqrt[4]{ (\frac{2}{3})^{8} }\\= (\frac{2}{3})^{\frac{8}{4}}\\= (\frac{2}{3})^{2}=\frac{4}{9}\)
11. \(\sqrt[4]{ (\frac{19}{20})^{8} }\\= (\frac{19}{20})^{\frac{8}{4}}\\= (\frac{19}{20})^{2}=\frac{361}{400}\)
12. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)