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

1. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
3. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
4. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
5. \(\sqrt[4]{ (\frac{2}{3})^{12} }\)
6. \( \sqrt{ (\frac{3}{2})^{-8} } \)
7. \( \sqrt{ (\frac{19}{20})^{4} } \)
8. \(\sqrt[4]{ (\frac{5}{4})^{8} }\)
9. \(\sqrt[6]{ (8)^{2} }\)
10. \(\sqrt[6]{ (\frac{49}{81})^{3} }\)
11. \(\sqrt[4]{ (\frac{17}{19})^{8} }\)
12. \(\sqrt[8]{ (\frac{169}{361})^{4} }\)

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

Verbetersleutel

1. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{4}{12}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
3. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
4. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
5. \(\sqrt[4]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{4}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
6. \( \sqrt{ (\frac{3}{2})^{-8} } \\= (\frac{3}{2})^{\frac{-8}{2}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
7. \( \sqrt{ (\frac{19}{20})^{4} } \\= (\frac{19}{20})^{\frac{4}{2}}\\= (\frac{19}{20})^{2}=\frac{361}{400}\)
8. \(\sqrt[4]{ (\frac{5}{4})^{8} }\\= (\frac{5}{4})^{\frac{8}{4}}\\= (\frac{5}{4})^{2}=\frac{25}{16}\)
9. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
10. \(\sqrt[6]{ (\frac{49}{81})^{3} }\\= (\frac{49}{81})^{\frac{-3}{6}}\\= (\frac{49}{81})^{\frac{-1}{2}}\\= \sqrt{ \frac{81}{49} } =\frac{9}{7}\)
11. \(\sqrt[4]{ (\frac{17}{19})^{8} }\\= (\frac{17}{19})^{\frac{8}{4}}\\= (\frac{17}{19})^{2}=\frac{289}{361}\)
12. \(\sqrt[8]{ (\frac{169}{361})^{4} }\\= (\frac{169}{361})^{\frac{4}{8}}\\= (\frac{169}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{169}{361} } =\frac{13}{19}\)