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

1. \( \sqrt{ (\frac{16}{19})^{-4} } \)
2. \(\sqrt[4]{ (\frac{1}{2})^{12} }\)
3. \( \sqrt{ (\frac{13}{20})^{4} } \)
4. \( \sqrt{ (\frac{12}{17})^{4} } \)
5. \( \sqrt{ (\frac{10}{17})^{4} } \)
6. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
7. \(\sqrt[3]{ (\frac{3}{4})^{9} }\)
8. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
9. \( \sqrt{ (\frac{18}{19})^{4} } \)
10. \(\sqrt[3]{ (\frac{13}{16})^{-6} }\)
11. \(\sqrt[4]{ (\frac{17}{19})^{-8} }\)
12. \(\sqrt[4]{ (\frac{2}{9})^{8} }\)

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

Verbetersleutel

1. \( \sqrt{ (\frac{16}{19})^{-4} } \\= (\frac{16}{19})^{\frac{-4}{2}}\\= (\frac{16}{19})^{-2}\\= (\frac{19}{16})^{2}= \frac{361}{256}\)
2. \(\sqrt[4]{ (\frac{1}{2})^{12} }\\= (\frac{1}{2})^{\frac{12}{4}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
3. \( \sqrt{ (\frac{13}{20})^{4} } \\= (\frac{13}{20})^{\frac{4}{2}}\\= (\frac{13}{20})^{2}=\frac{169}{400}\)
4. \( \sqrt{ (\frac{12}{17})^{4} } \\= (\frac{12}{17})^{\frac{4}{2}}\\= (\frac{12}{17})^{2}=\frac{144}{289}\)
5. \( \sqrt{ (\frac{10}{17})^{4} } \\= (\frac{10}{17})^{\frac{4}{2}}\\= (\frac{10}{17})^{2}=\frac{100}{289}\)
6. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{-4}{16}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
7. \(\sqrt[3]{ (\frac{3}{4})^{9} }\\= (\frac{3}{4})^{\frac{9}{3}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
8. \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
9. \( \sqrt{ (\frac{18}{19})^{4} } \\= (\frac{18}{19})^{\frac{4}{2}}\\= (\frac{18}{19})^{2}=\frac{324}{361}\)
10. \(\sqrt[3]{ (\frac{13}{16})^{-6} }\\= (\frac{13}{16})^{\frac{-6}{3}}\\= (\frac{13}{16})^{-2}\\= (\frac{16}{13})^{2}= \frac{256}{169}\)
11. \(\sqrt[4]{ (\frac{17}{19})^{-8} }\\= (\frac{17}{19})^{\frac{-8}{4}}\\= (\frac{17}{19})^{-2}\\= (\frac{19}{17})^{2}= \frac{361}{289}\)
12. \(\sqrt[4]{ (\frac{2}{9})^{8} }\\= (\frac{2}{9})^{\frac{8}{4}}\\= (\frac{2}{9})^{2}=\frac{4}{81}\)