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

1. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
2. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
3. \( \sqrt{ (\frac{2}{3})^{6} } \)
4. \(\sqrt[6]{ (8)^{2} }\)
5. \( \sqrt{ (\frac{3}{2})^{-8} } \)
6. \(\sqrt[6]{ (\frac{81}{100})^{3} }\)
7. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\)
8. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
9. \(\sqrt[3]{ (\frac{1}{2})^{-9} }\)
10. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
11. \(\sqrt[3]{ (\frac{14}{19})^{6} }\)
12. \( \sqrt{ (\frac{3}{2})^{8} } \)

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

Verbetersleutel

1. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{2}{8}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
2. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{-3}{9}}\\= (\frac{8}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{8} }=\frac{3}{2}\)
3. \( \sqrt{ (\frac{2}{3})^{6} } \\= (\frac{2}{3})^{\frac{6}{2}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
4. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
5. \( \sqrt{ (\frac{3}{2})^{-8} } \\= (\frac{3}{2})^{\frac{-8}{2}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
6. \(\sqrt[6]{ (\frac{81}{100})^{3} }\\= (\frac{81}{100})^{\frac{3}{6}}\\= (\frac{81}{100})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{100} } =\frac{9}{10}\)
7. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\\= (\frac{2}{3})^{\frac{-16}{4}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
8. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{-2}{8}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
9. \(\sqrt[3]{ (\frac{1}{2})^{-9} }\\= (\frac{1}{2})^{\frac{-9}{3}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
10. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
11. \(\sqrt[3]{ (\frac{14}{19})^{6} }\\= (\frac{14}{19})^{\frac{6}{3}}\\= (\frac{14}{19})^{2}=\frac{196}{361}\)
12. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)