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

1. \(\sqrt[4]{ (\frac{49}{361})^{2} }\)
2. \(\sqrt[6]{ (\frac{100}{361})^{3} }\)
3. \( \sqrt{ (\frac{3}{2})^{8} } \)
4. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
5. \(\sqrt[6]{ (\frac{1}{4})^{3} }\)
6. \(\sqrt[8]{ (\frac{361}{400})^{4} }\)
7. \(\sqrt[3]{ (\frac{10}{9})^{6} }\)
8. \(\sqrt[9]{ (\frac{64}{27})^{3} }\)
9. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
10. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\)
11. \(\sqrt[8]{ (\frac{36}{49})^{4} }\)
12. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{49}{361})^{2} }\\= (\frac{49}{361})^{\frac{2}{4}}\\= (\frac{49}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{49}{361} } =\frac{7}{19}\)
2. \(\sqrt[6]{ (\frac{100}{361})^{3} }\\= (\frac{100}{361})^{\frac{3}{6}}\\= (\frac{100}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{100}{361} } =\frac{10}{19}\)
3. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
4. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
5. \(\sqrt[6]{ (\frac{1}{4})^{3} }\\= (\frac{1}{4})^{\frac{3}{6}}\\= (\frac{1}{4})^{\frac{1}{2}}\\= \sqrt{ \frac{1}{4} } =\frac{1}{2}\)
6. \(\sqrt[8]{ (\frac{361}{400})^{4} }\\= (\frac{361}{400})^{\frac{4}{8}}\\= (\frac{361}{400})^{\frac{1}{2}}\\= \sqrt{ \frac{361}{400} } =\frac{19}{20}\)
7. \(\sqrt[3]{ (\frac{10}{9})^{6} }\\= (\frac{10}{9})^{\frac{6}{3}}\\= (\frac{10}{9})^{2}=\frac{100}{81}\)
8. \(\sqrt[9]{ (\frac{64}{27})^{3} }\\= (\frac{64}{27})^{\frac{3}{9}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
9. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{-3}{12}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
10. \(\sqrt[4]{ (\frac{2}{3})^{-16} }\\= (\frac{2}{3})^{\frac{-16}{4}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
11. \(\sqrt[8]{ (\frac{36}{49})^{4} }\\= (\frac{36}{49})^{\frac{4}{8}}\\= (\frac{36}{49})^{\frac{1}{2}}\\= \sqrt{ \frac{36}{49} } =\frac{6}{7}\)
12. \(\sqrt[8]{ (\frac{16}{81})^{2} }\\= (\frac{16}{81})^{\frac{2}{8}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)