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

1. \( \sqrt{ (\frac{2}{3})^{8} } \)
2. \(\sqrt[4]{ (\frac{10}{17})^{8} }\)
3. \(\sqrt[3]{ (\frac{1}{2})^{-9} }\)
4. \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
5. \(\sqrt[3]{ (\frac{1}{2})^{9} }\)
6. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
7. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
8. \(\sqrt[3]{ (\frac{4}{3})^{9} }\)
9. \(\sqrt[3]{ (\frac{2}{3})^{12} }\)
10. \(\sqrt[4]{ (2)^{12} }\)
11. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
12. \(\sqrt[3]{ (\frac{18}{19})^{6} }\)

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

Verbetersleutel

1. \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
2. \(\sqrt[4]{ (\frac{10}{17})^{8} }\\= (\frac{10}{17})^{\frac{8}{4}}\\= (\frac{10}{17})^{2}=\frac{100}{289}\)
3. \(\sqrt[3]{ (\frac{1}{2})^{-9} }\\= (\frac{1}{2})^{\frac{-9}{3}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
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. \(\sqrt[3]{ (\frac{1}{2})^{9} }\\= (\frac{1}{2})^{\frac{9}{3}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
6. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{4}{12}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
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. \(\sqrt[3]{ (\frac{4}{3})^{9} }\\= (\frac{4}{3})^{\frac{9}{3}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
9. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
10. \(\sqrt[4]{ (2)^{12} }\\= (2)^{\frac{12}{4}}\\= (2)^{3}=8\)
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. \(\sqrt[3]{ (\frac{18}{19})^{6} }\\= (\frac{18}{19})^{\frac{6}{3}}\\= (\frac{18}{19})^{2}=\frac{324}{361}\)