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

1. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
2. \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
3. \(\sqrt[12]{ (\frac{27}{64})^{4} }\)
4. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
5. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
6. \(\sqrt[4]{ (\frac{6}{17})^{8} }\)
7. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
8. \( \sqrt{ (\frac{2}{3})^{-8} } \)
9. \(\sqrt[8]{ (\frac{49}{225})^{4} }\)
10. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
11. \(\sqrt[3]{ (\frac{3}{4})^{6} }\)
12. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
2. \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
3. \(\sqrt[12]{ (\frac{27}{64})^{4} }\\= (\frac{27}{64})^{\frac{4}{12}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
4. \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
5. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
6. \(\sqrt[4]{ (\frac{6}{17})^{8} }\\= (\frac{6}{17})^{\frac{8}{4}}\\= (\frac{6}{17})^{2}=\frac{36}{289}\)
7. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \( \sqrt{ (\frac{2}{3})^{-8} } \\= (\frac{2}{3})^{\frac{-8}{2}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
9. \(\sqrt[8]{ (\frac{49}{225})^{4} }\\= (\frac{49}{225})^{\frac{4}{8}}\\= (\frac{49}{225})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{225} } =\frac{7}{15}\)
10. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{4}{16}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
11. \(\sqrt[3]{ (\frac{3}{4})^{6} }\\= (\frac{3}{4})^{\frac{6}{3}}\\= (\frac{3}{4})^{2}=\frac{9}{16}\)
12. \(\sqrt[3]{ (\frac{3}{2})^{-12} }\\= (\frac{3}{2})^{\frac{-12}{3}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)