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

1. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
2. \(\sqrt[12]{ (\frac{1}{8})^{4} }\)
3. \( \sqrt{ (\frac{4}{5})^{4} } \)
4. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
5. \( \sqrt{ (\frac{3}{5})^{-4} } \)
6. \( \sqrt{ (\frac{3}{2})^{-8} } \)
7. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
8. \(\sqrt[9]{ (8)^{3} }\)
9. \( \sqrt{ (\frac{2}{3})^{6} } \)
10. \(\sqrt[3]{ (\frac{3}{4})^{9} }\)
11. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
12. \( \sqrt{ (\frac{15}{17})^{4} } \)

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
2. \(\sqrt[12]{ (\frac{1}{8})^{4} }\\= (\frac{1}{8})^{\frac{4}{12}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
3. \( \sqrt{ (\frac{4}{5})^{4} } \\= (\frac{4}{5})^{\frac{4}{2}}\\= (\frac{4}{5})^{2}=\frac{16}{25}\)
4. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
5. \( \sqrt{ (\frac{3}{5})^{-4} } \\= (\frac{3}{5})^{\frac{-4}{2}}\\= (\frac{3}{5})^{-2}\\= (\frac{5}{3})^{2}= \frac{25}{9}\)
6. \( \sqrt{ (\frac{3}{2})^{-8} } \\= (\frac{3}{2})^{\frac{-8}{2}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
7. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
8. \(\sqrt[9]{ (8)^{3} }\\= (8)^{\frac{3}{9}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
9. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
10. \(\sqrt[3]{ (\frac{3}{4})^{9} }\\= (\frac{3}{4})^{\frac{9}{3}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
11. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
12. \( \sqrt{ (\frac{15}{17})^{4} } \\= (\frac{15}{17})^{\frac{4}{2}}\\= (\frac{15}{17})^{2}=\frac{225}{289}\)