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

1. \( \sqrt{ (\frac{3}{2})^{8} } \)
2. \(\sqrt[4]{ (2)^{-12} }\)
3. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\)
4. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
5. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)
6. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
7. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
8. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
9. \(\sqrt[4]{ (\frac{1}{5})^{8} }\)
10. \(\sqrt[8]{ (\frac{121}{144})^{4} }\)
11. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
12. \( \sqrt{ (\frac{4}{3})^{6} } \)

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

Verbetersleutel

1. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
2. \(\sqrt[4]{ (2)^{-12} }\\= (2)^{\frac{-12}{4}}\\= (2)^{-3}\\= (\frac{1}{2})^{3}= \frac{1}{8}\)
3. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\\= (\frac{3}{2})^{\frac{-16}{4}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
4. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
5. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
6. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
7. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
8. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{-4}{16}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
9. \(\sqrt[4]{ (\frac{1}{5})^{8} }\\= (\frac{1}{5})^{\frac{8}{4}}\\= (\frac{1}{5})^{2}=\frac{1}{25}\)
10. \(\sqrt[8]{ (\frac{121}{144})^{4} }\\= (\frac{121}{144})^{\frac{4}{8}}\\= (\frac{121}{144})^{\frac{1}{2}}\\= \sqrt{ \frac{121}{144} } =\frac{11}{12}\)
11. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{4}{12}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
12. \( \sqrt{ (\frac{4}{3})^{6} } \\= (\frac{4}{3})^{\frac{6}{2}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)