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

1. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)
2. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
3. \( \sqrt{ (\frac{4}{3})^{6} } \)
4. \( \sqrt{ (\frac{3}{4})^{-6} } \)
5. \(\sqrt[6]{ (\frac{16}{49})^{3} }\)
6. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
7. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
8. \( \sqrt{ (\frac{1}{2})^{-6} } \)
9. \(\sqrt[3]{ (2)^{-9} }\)
10. \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
11. \(\sqrt[8]{ (\frac{256}{361})^{4} }\)
12. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)

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

Verbetersleutel

1. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
2. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
3. \( \sqrt{ (\frac{4}{3})^{6} } \\= (\frac{4}{3})^{\frac{6}{2}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
4. \( \sqrt{ (\frac{3}{4})^{-6} } \\= (\frac{3}{4})^{\frac{-6}{2}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
5. \(\sqrt[6]{ (\frac{16}{49})^{3} }\\= (\frac{16}{49})^{\frac{3}{6}}\\= (\frac{16}{49})^{\frac{1}{2}}\\= \sqrt{ \frac{16}{49} } =\frac{4}{7}\)
6. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{-3}{12}}\\= (\frac{16}{81})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
7. \(\sqrt[16]{ (\frac{16}{81})^{4} }\\= (\frac{16}{81})^{\frac{4}{16}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \( \sqrt{ (\frac{1}{2})^{-6} } \\= (\frac{1}{2})^{\frac{-6}{2}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
9. \(\sqrt[3]{ (2)^{-9} }\\= (2)^{\frac{-9}{3}}\\= (2)^{-3}\\= (\frac{1}{2})^{3}= \frac{1}{8}\)
10. \(\sqrt[9]{ (\frac{27}{64})^{3} }\\= (\frac{27}{64})^{\frac{3}{9}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
11. \(\sqrt[8]{ (\frac{256}{361})^{4} }\\= (\frac{256}{361})^{\frac{-4}{8}}\\= (\frac{256}{361})^{\frac{-1}{2}}\\= \sqrt{ \frac{361}{256} } =\frac{19}{16}\)
12. \(\sqrt[4]{ (\frac{3}{4})^{12} }\\= (\frac{3}{4})^{\frac{12}{4}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)