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

1. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
3. \( \sqrt{ (\frac{19}{20})^{4} } \)
4. \(\sqrt[8]{ (\frac{36}{49})^{4} }\)
5. \(\sqrt[6]{ (\frac{4}{49})^{3} }\)
6. \(\sqrt[8]{ (\frac{16}{25})^{4} }\)
7. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
8. \(\sqrt[4]{ (2)^{12} }\)
9. \( \sqrt{ (\frac{3}{2})^{8} } \)
10. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
11. \( \sqrt{ (2)^{6} } \)
12. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)

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

Verbetersleutel

1. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{4}{12}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
2. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
3. \( \sqrt{ (\frac{19}{20})^{4} } \\= (\frac{19}{20})^{\frac{4}{2}}\\= (\frac{19}{20})^{2}=\frac{361}{400}\)
4. \(\sqrt[8]{ (\frac{36}{49})^{4} }\\= (\frac{36}{49})^{\frac{-4}{8}}\\= (\frac{36}{49})^{\frac{-1}{2}}\\= \sqrt{ \frac{49}{36} } =\frac{7}{6}\)
5. \(\sqrt[6]{ (\frac{4}{49})^{3} }\\= (\frac{4}{49})^{\frac{-3}{6}}\\= (\frac{4}{49})^{\frac{-1}{2}}\\= \sqrt{ \frac{49}{4} } =\frac{7}{2}\)
6. \(\sqrt[8]{ (\frac{16}{25})^{4} }\\= (\frac{16}{25})^{\frac{4}{8}}\\= (\frac{16}{25})^{\frac{1}{2}}\\= \sqrt{ \frac{16}{25} } =\frac{4}{5}\)
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. \(\sqrt[4]{ (2)^{12} }\\= (2)^{\frac{12}{4}}\\= (2)^{3}=8\)
9. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
10. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{-4}{16}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
11. \( \sqrt{ (2)^{6} } \\= (2)^{\frac{6}{2}}\\= (2)^{3}=8\)
12. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)