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

1. \(\sqrt[4]{ (\frac{4}{3})^{12} }\)
2. \(\sqrt[6]{ (\frac{169}{225})^{3} }\)
3. \(\sqrt[12]{ (8)^{4} }\)
4. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
5. \(\sqrt[4]{ (\frac{5}{6})^{-8} }\)
6. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
7. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
8. \( \sqrt{ (\frac{16}{19})^{-4} } \)
9. \(\sqrt[4]{ (\frac{169}{400})^{2} }\)
10. \(\sqrt[4]{ (\frac{169}{256})^{2} }\)
11. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
12. \(\sqrt[4]{ (\frac{9}{14})^{8} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{4}{3})^{12} }\\= (\frac{4}{3})^{\frac{12}{4}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
2. \(\sqrt[6]{ (\frac{169}{225})^{3} }\\= (\frac{169}{225})^{\frac{-3}{6}}\\= (\frac{169}{225})^{\frac{-1}{2}}\\= \sqrt{ \frac{225}{169} } =\frac{15}{13}\)
3. \(\sqrt[12]{ (8)^{4} }\\= (8)^{\frac{-4}{12}}\\= (8)^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
4. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
5. \(\sqrt[4]{ (\frac{5}{6})^{-8} }\\= (\frac{5}{6})^{\frac{-8}{4}}\\= (\frac{5}{6})^{-2}\\= (\frac{6}{5})^{2}= \frac{36}{25}\)
6. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
7. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{2}{8}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \( \sqrt{ (\frac{16}{19})^{-4} } \\= (\frac{16}{19})^{\frac{-4}{2}}\\= (\frac{16}{19})^{-2}\\= (\frac{19}{16})^{2}= \frac{361}{256}\)
9. \(\sqrt[4]{ (\frac{169}{400})^{2} }\\= (\frac{169}{400})^{\frac{-2}{4}}\\= (\frac{169}{400})^{\frac{-1}{2}}\\= \sqrt{ \frac{400}{169} } =\frac{20}{13}\)
10. \(\sqrt[4]{ (\frac{169}{256})^{2} }\\= (\frac{169}{256})^{\frac{2}{4}}\\= (\frac{169}{256})^{\frac{1}{2}}\\= \sqrt{ \frac{169}{256} } =\frac{13}{16}\)
11. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
12. \(\sqrt[4]{ (\frac{9}{14})^{8} }\\= (\frac{9}{14})^{\frac{8}{4}}\\= (\frac{9}{14})^{2}=\frac{81}{196}\)