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

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

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

Verbetersleutel

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