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

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

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

Verbetersleutel

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