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

1. \(\sqrt[12]{ (\frac{27}{64})^{4} }\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
3. \(\sqrt[4]{ (\frac{81}{121})^{2} }\)
4. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
5. \(\sqrt[6]{ (8)^{2} }\)
6. \(\sqrt[8]{ (\frac{400}{289})^{4} }\)
7. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
8. \(\sqrt[9]{ (\frac{64}{27})^{3} }\)
9. \(\sqrt[6]{ (\frac{4}{361})^{3} }\)
10. \( \sqrt{ (\frac{11}{15})^{-4} } \)
11. \(\sqrt[8]{ (\frac{49}{64})^{4} }\)
12. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)

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

Verbetersleutel

1. \(\sqrt[12]{ (\frac{27}{64})^{4} }\\= (\frac{27}{64})^{\frac{-4}{12}}\\= (\frac{27}{64})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
3. \(\sqrt[4]{ (\frac{81}{121})^{2} }\\= (\frac{81}{121})^{\frac{2}{4}}\\= (\frac{81}{121})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{121} } =\frac{9}{11}\)
4. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
5. \(\sqrt[6]{ (8)^{2} }\\= (8)^{\frac{2}{6}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
6. \(\sqrt[8]{ (\frac{400}{289})^{4} }\\= (\frac{400}{289})^{\frac{4}{8}}\\= (\frac{400}{289})^{\frac{1}{2}}\\= \sqrt{ \frac{400}{289} } =\frac{20}{17}\)
7. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
8. \(\sqrt[9]{ (\frac{64}{27})^{3} }\\= (\frac{64}{27})^{\frac{-3}{9}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
9. \(\sqrt[6]{ (\frac{4}{361})^{3} }\\= (\frac{4}{361})^{\frac{3}{6}}\\= (\frac{4}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{4}{361} } =\frac{2}{19}\)
10. \( \sqrt{ (\frac{11}{15})^{-4} } \\= (\frac{11}{15})^{\frac{-4}{2}}\\= (\frac{11}{15})^{-2}\\= (\frac{15}{11})^{2}= \frac{225}{121}\)
11. \(\sqrt[8]{ (\frac{49}{64})^{4} }\\= (\frac{49}{64})^{\frac{-4}{8}}\\= (\frac{49}{64})^{\frac{-1}{2}}\\= \sqrt{ \frac{64}{49} } =\frac{8}{7}\)
12. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{-4}{16}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)