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

1. \(\sqrt[8]{ (\frac{1}{25})^{4} }\)
2. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
3. \(\sqrt[3]{ (\frac{12}{13})^{6} }\)
4. \(\sqrt[4]{ (\frac{361}{400})^{2} }\)
5. \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
6. \( \sqrt{ (\frac{5}{8})^{-4} } \)
7. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
8. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\)
9. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
10. \(\sqrt[4]{ (\frac{2}{5})^{-8} }\)
11. \(\sqrt[4]{ (\frac{289}{361})^{2} }\)
12. \( \sqrt{ (\frac{2}{3})^{6} } \)

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

Verbetersleutel

1. \(\sqrt[8]{ (\frac{1}{25})^{4} }\\= (\frac{1}{25})^{\frac{-4}{8}}\\= (\frac{1}{25})^{\frac{-1}{2}}\\= \sqrt{ 25 } =5\)
2. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{-2}{6}}\\= (\frac{27}{64})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
3. \(\sqrt[3]{ (\frac{12}{13})^{6} }\\= (\frac{12}{13})^{\frac{6}{3}}\\= (\frac{12}{13})^{2}=\frac{144}{169}\)
4. \(\sqrt[4]{ (\frac{361}{400})^{2} }\\= (\frac{361}{400})^{\frac{2}{4}}\\= (\frac{361}{400})^{\frac{1}{2}}\\= \sqrt{ \frac{361}{400} } =\frac{19}{20}\)
5. \(\sqrt[9]{ (\frac{27}{64})^{3} }\\= (\frac{27}{64})^{\frac{3}{9}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
6. \( \sqrt{ (\frac{5}{8})^{-4} } \\= (\frac{5}{8})^{\frac{-4}{2}}\\= (\frac{5}{8})^{-2}\\= (\frac{8}{5})^{2}= \frac{64}{25}\)
7. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
8. \(\sqrt[4]{ (\frac{3}{4})^{-12} }\\= (\frac{3}{4})^{\frac{-12}{4}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
9. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
10. \(\sqrt[4]{ (\frac{2}{5})^{-8} }\\= (\frac{2}{5})^{\frac{-8}{4}}\\= (\frac{2}{5})^{-2}\\= (\frac{5}{2})^{2}= \frac{25}{4}\)
11. \(\sqrt[4]{ (\frac{289}{361})^{2} }\\= (\frac{289}{361})^{\frac{2}{4}}\\= (\frac{289}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{289}{361} } =\frac{17}{19}\)
12. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)