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

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
2. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\)
3. \( \sqrt{ (\frac{3}{2})^{8} } \)
4. \(\sqrt[4]{ (\frac{100}{361})^{2} }\)
5. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
6. \(\sqrt[4]{ (\frac{2}{9})^{8} }\)
7. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
8. \(\sqrt[4]{ (\frac{1}{2})^{12} }\)
9. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
10. \(\sqrt[3]{ (\frac{4}{3})^{-6} }\)
11. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
12. \(\sqrt[4]{ (\frac{5}{8})^{8} }\)

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

Verbetersleutel

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
2. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\\= (\frac{3}{2})^{\frac{-12}{3}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
3. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
4. \(\sqrt[4]{ (\frac{100}{361})^{2} }\\= (\frac{100}{361})^{\frac{2}{4}}\\= (\frac{100}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{100}{361} } =\frac{10}{19}\)
5. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{4}{12}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
6. \(\sqrt[4]{ (\frac{2}{9})^{8} }\\= (\frac{2}{9})^{\frac{8}{4}}\\= (\frac{2}{9})^{2}=\frac{4}{81}\)
7. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
8. \(\sqrt[4]{ (\frac{1}{2})^{12} }\\= (\frac{1}{2})^{\frac{12}{4}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
9. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
10. \(\sqrt[3]{ (\frac{4}{3})^{-6} }\\= (\frac{4}{3})^{\frac{-6}{3}}\\= (\frac{4}{3})^{-2}\\= (\frac{3}{4})^{2}= \frac{9}{16}\)
11. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
12. \(\sqrt[4]{ (\frac{5}{8})^{8} }\\= (\frac{5}{8})^{\frac{8}{4}}\\= (\frac{5}{8})^{2}=\frac{25}{64}\)