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

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

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

Verbetersleutel

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