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

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\)
2. \( \sqrt{ (\frac{2}{19})^{4} } \)
3. \(\sqrt[4]{ (2)^{12} }\)
4. \(\sqrt[16]{ (\frac{16}{81})^{4} }\)
5. \(\sqrt[12]{ (8)^{4} }\)
6. \(\sqrt[3]{ (\frac{2}{3})^{9} }\)
7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\)
8. \( \sqrt{ (\frac{1}{2})^{-6} } \)
9. \(\sqrt[8]{ (\frac{9}{49})^{4} }\)
10. \(\sqrt[12]{ (\frac{64}{27})^{4} }\)
11. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
12. \(\sqrt[3]{ (\frac{13}{16})^{6} }\)

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

Verbetersleutel

1. \(\sqrt[16]{ (\frac{81}{16})^{4} }\\= (\frac{81}{16})^{\frac{-4}{16}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
2. \( \sqrt{ (\frac{2}{19})^{4} } \\= (\frac{2}{19})^{\frac{4}{2}}\\= (\frac{2}{19})^{2}=\frac{4}{361}\)
3. \(\sqrt[4]{ (2)^{12} }\\= (2)^{\frac{12}{4}}\\= (2)^{3}=8\)
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. \(\sqrt[12]{ (8)^{4} }\\= (8)^{\frac{-4}{12}}\\= (8)^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)
6. \(\sqrt[3]{ (\frac{2}{3})^{9} }\\= (\frac{2}{3})^{\frac{9}{3}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
7. \(\sqrt[8]{ (\frac{81}{16})^{2} }\\= (\frac{81}{16})^{\frac{-2}{8}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
8. \( \sqrt{ (\frac{1}{2})^{-6} } \\= (\frac{1}{2})^{\frac{-6}{2}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
9. \(\sqrt[8]{ (\frac{9}{49})^{4} }\\= (\frac{9}{49})^{\frac{-4}{8}}\\= (\frac{9}{49})^{\frac{-1}{2}}\\= \sqrt{ \frac{49}{9} } =\frac{7}{3}\)
10. \(\sqrt[12]{ (\frac{64}{27})^{4} }\\= (\frac{64}{27})^{\frac{4}{12}}\\= (\frac{64}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{64}{27} }=\frac{4}{3}\)
11. \(\sqrt[4]{ (\frac{2}{3})^{16} }\\= (\frac{2}{3})^{\frac{16}{4}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
12. \(\sqrt[3]{ (\frac{13}{16})^{6} }\\= (\frac{13}{16})^{\frac{6}{3}}\\= (\frac{13}{16})^{2}=\frac{169}{256}\)