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

1. \(\sqrt[3]{ (\frac{2}{3})^{-9} }\)
2. \(\sqrt[6]{ (\frac{289}{324})^{3} }\)
3. \(\sqrt[6]{ (\frac{361}{400})^{3} }\)
4. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
5. \( \sqrt{ (\frac{2}{3})^{-8} } \)
6. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
7. \(\sqrt[6]{ (\frac{49}{289})^{3} }\)
8. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\)
9. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
10. \(\sqrt[6]{ (\frac{400}{289})^{3} }\)
11. \(\sqrt[9]{ (\frac{1}{8})^{3} }\)
12. \(\sqrt[4]{ (\frac{324}{361})^{2} }\)

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{2}{3})^{-9} }\\= (\frac{2}{3})^{\frac{-9}{3}}\\= (\frac{2}{3})^{-3}\\= (\frac{3}{2})^{3}= \frac{27}{8}\)
2. \(\sqrt[6]{ (\frac{289}{324})^{3} }\\= (\frac{289}{324})^{\frac{3}{6}}\\= (\frac{289}{324})^{\frac{1}{2}}\\= \sqrt{ \frac{289}{324} } =\frac{17}{18}\)
3. \(\sqrt[6]{ (\frac{361}{400})^{3} }\\= (\frac{361}{400})^{\frac{3}{6}}\\= (\frac{361}{400})^{\frac{1}{2}}\\= \sqrt{ \frac{361}{400} } =\frac{19}{20}\)
4. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
5. \( \sqrt{ (\frac{2}{3})^{-8} } \\= (\frac{2}{3})^{\frac{-8}{2}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
6. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
7. \(\sqrt[6]{ (\frac{49}{289})^{3} }\\= (\frac{49}{289})^{\frac{3}{6}}\\= (\frac{49}{289})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{289} } =\frac{7}{17}\)
8. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\\= (\frac{2}{3})^{\frac{-16}{4}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
9. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
10. \(\sqrt[6]{ (\frac{400}{289})^{3} }\\= (\frac{400}{289})^{\frac{-3}{6}}\\= (\frac{400}{289})^{\frac{-1}{2}}\\= \sqrt{ \frac{289}{400} } =\frac{17}{20}\)
11. \(\sqrt[9]{ (\frac{1}{8})^{3} }\\= (\frac{1}{8})^{\frac{3}{9}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
12. \(\sqrt[4]{ (\frac{324}{361})^{2} }\\= (\frac{324}{361})^{\frac{2}{4}}\\= (\frac{324}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{324}{361} } =\frac{18}{19}\)