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

1. \( \sqrt{ (2)^{6} } \)
2. \(\sqrt[6]{ (8)^{2} }\)
3. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
4. \(\sqrt[12]{ (\frac{1}{8})^{4} }\)
5. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\)
6. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
7. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
8. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)
9. \(\sqrt[3]{ (\frac{4}{3})^{9} }\)
10. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
11. \(\sqrt[3]{ (\frac{3}{17})^{6} }\)
12. \( \sqrt{ (\frac{3}{4})^{6} } \)

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

Verbetersleutel

1. \( \sqrt{ (2)^{6} } \\= (2)^{\frac{6}{2}}\\= (2)^{3}=8\)
2. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
3. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
4. \(\sqrt[12]{ (\frac{1}{8})^{4} }\\= (\frac{1}{8})^{\frac{4}{12}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
5. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\\= (\frac{3}{4})^{\frac{-9}{3}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
6. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
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. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{-4}{12}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
9. \(\sqrt[3]{ (\frac{4}{3})^{9} }\\= (\frac{4}{3})^{\frac{9}{3}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
10. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
11. \(\sqrt[3]{ (\frac{3}{17})^{6} }\\= (\frac{3}{17})^{\frac{6}{3}}\\= (\frac{3}{17})^{2}=\frac{9}{289}\)
12. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)