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

1. \(\sqrt[4]{ (\frac{400}{289})^{2} }\)
2. \(\sqrt[3]{ (\frac{2}{17})^{6} }\)
3. \(\sqrt[4]{ (\frac{49}{100})^{2} }\)
4. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\)
5. \( \sqrt{ (\frac{2}{3})^{-8} } \)
6. \(\sqrt[3]{ (\frac{5}{7})^{6} }\)
7. \( \sqrt{ (\frac{3}{4})^{6} } \)
8. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\)
9. \(\sqrt[8]{ (\frac{169}{324})^{4} }\)
10. \( \sqrt{ (\frac{3}{2})^{8} } \)
11. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
12. \(\sqrt[12]{ (8)^{4} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{400}{289})^{2} }\\= (\frac{400}{289})^{\frac{-2}{4}}\\= (\frac{400}{289})^{\frac{-1}{2}}\\= \sqrt{ \frac{289}{400} } =\frac{17}{20}\)
2. \(\sqrt[3]{ (\frac{2}{17})^{6} }\\= (\frac{2}{17})^{\frac{6}{3}}\\= (\frac{2}{17})^{2}=\frac{4}{289}\)
3. \(\sqrt[4]{ (\frac{49}{100})^{2} }\\= (\frac{49}{100})^{\frac{-2}{4}}\\= (\frac{49}{100})^{\frac{-1}{2}}\\= \sqrt{ \frac{100}{49} } =\frac{10}{7}\)
4. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\\= (\frac{3}{2})^{\frac{-12}{3}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
5. \( \sqrt{ (\frac{2}{3})^{-8} } \\= (\frac{2}{3})^{\frac{-8}{2}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
6. \(\sqrt[3]{ (\frac{5}{7})^{6} }\\= (\frac{5}{7})^{\frac{6}{3}}\\= (\frac{5}{7})^{2}=\frac{25}{49}\)
7. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
8. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\\= (\frac{3}{2})^{\frac{-16}{4}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
9. \(\sqrt[8]{ (\frac{169}{324})^{4} }\\= (\frac{169}{324})^{\frac{-4}{8}}\\= (\frac{169}{324})^{\frac{-1}{2}}\\= \sqrt{ \frac{324}{169} } =\frac{18}{13}\)
10. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
11. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
12. \(\sqrt[12]{ (8)^{4} }\\= (8)^{\frac{4}{12}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)