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

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

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{18}{19})^{-6} }\\= (\frac{18}{19})^{\frac{-6}{3}}\\= (\frac{18}{19})^{-2}\\= (\frac{19}{18})^{2}= \frac{361}{324}\)
2. \(\sqrt[4]{ (\frac{7}{12})^{8} }\\= (\frac{7}{12})^{\frac{8}{4}}\\= (\frac{7}{12})^{2}=\frac{49}{144}\)
3. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
4. \( \sqrt{ (\frac{4}{3})^{-6} } \\= (\frac{4}{3})^{\frac{-6}{2}}\\= (\frac{4}{3})^{-3}\\= (\frac{3}{4})^{3}= \frac{27}{64}\)
5. \(\sqrt[12]{ (8)^{4} }\\= (8)^{\frac{4}{12}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
6. \(\sqrt[3]{ (\frac{5}{16})^{-6} }\\= (\frac{5}{16})^{\frac{-6}{3}}\\= (\frac{5}{16})^{-2}\\= (\frac{16}{5})^{2}= \frac{256}{25}\)
7. \(\sqrt[12]{ (\frac{27}{64})^{4} }\\= (\frac{27}{64})^{\frac{4}{12}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
8. \(\sqrt[8]{ (\frac{49}{361})^{4} }\\= (\frac{49}{361})^{\frac{4}{8}}\\= (\frac{49}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{361} } =\frac{7}{19}\)
9. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
10. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
11. \(\sqrt[3]{ (\frac{7}{9})^{6} }\\= (\frac{7}{9})^{\frac{6}{3}}\\= (\frac{7}{9})^{2}=\frac{49}{81}\)
12. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{-3}{12}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)