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

1. \(\sqrt[4]{ (\frac{17}{20})^{8} }\)
2. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
3. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
4. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
5. \(\sqrt[8]{ (\frac{64}{121})^{4} }\)
6. \( \sqrt{ (\frac{3}{5})^{4} } \)
7. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
8. \(\sqrt[4]{ (\frac{81}{100})^{2} }\)
9. \(\sqrt[6]{ (\frac{81}{100})^{3} }\)
10. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
11. \(\sqrt[8]{ (\frac{81}{196})^{4} }\)
12. \(\sqrt[3]{ (2)^{9} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{17}{20})^{8} }\\= (\frac{17}{20})^{\frac{8}{4}}\\= (\frac{17}{20})^{2}=\frac{289}{400}\)
2. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
3. \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
4. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
5. \(\sqrt[8]{ (\frac{64}{121})^{4} }\\= (\frac{64}{121})^{\frac{4}{8}}\\= (\frac{64}{121})^{\frac{1}{2}}\\= \sqrt{ \frac{64}{121} } =\frac{8}{11}\)
6. \( \sqrt{ (\frac{3}{5})^{4} } \\= (\frac{3}{5})^{\frac{4}{2}}\\= (\frac{3}{5})^{2}=\frac{9}{25}\)
7. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
8. \(\sqrt[4]{ (\frac{81}{100})^{2} }\\= (\frac{81}{100})^{\frac{-2}{4}}\\= (\frac{81}{100})^{\frac{-1}{2}}\\= \sqrt{ \frac{100}{81} } =\frac{10}{9}\)
9. \(\sqrt[6]{ (\frac{81}{100})^{3} }\\= (\frac{81}{100})^{\frac{3}{6}}\\= (\frac{81}{100})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{100} } =\frac{9}{10}\)
10. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
11. \(\sqrt[8]{ (\frac{81}{196})^{4} }\\= (\frac{81}{196})^{\frac{4}{8}}\\= (\frac{81}{196})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{196} } =\frac{9}{14}\)
12. \(\sqrt[3]{ (2)^{9} }\\= (2)^{\frac{9}{3}}\\= (2)^{3}=8\)