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

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

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

Verbetersleutel

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