Getallen als grondtal

Hoofdmenu Eentje per keer  🖨

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

1. \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)
2. \(\sqrt[6]{ (\frac{64}{27})^{2} }\)
3. \(\sqrt[12]{ (\frac{8}{27})^{4} }\)
4. \( \sqrt{ (\frac{3}{2})^{8} } \)
5. \(\sqrt[4]{ (\frac{3}{2})^{16} }\)
6. \( \sqrt{ (\frac{4}{3})^{6} } \)
7. \(\sqrt[12]{ (\frac{81}{16})^{3} }\)
8. \( \sqrt{ (\frac{3}{4})^{6} } \)
9. \(\sqrt[9]{ (8)^{3} }\)
10. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\)
11. \(\sqrt[4]{ (\frac{13}{15})^{-8} }\)
12. \(\sqrt[4]{ (\frac{121}{169})^{2} }\)

---

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. \(\sqrt[6]{ (\frac{64}{27})^{2} }\\= (\frac{64}{27})^{\frac{-2}{6}}\\= (\frac{64}{27})^{\frac{-1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
3. \(\sqrt[12]{ (\frac{8}{27})^{4} }\\= (\frac{8}{27})^{\frac{4}{12}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
4. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
5. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
6. \( \sqrt{ (\frac{4}{3})^{6} } \\= (\frac{4}{3})^{\frac{6}{2}}\\= (\frac{4}{3})^{3}=\frac{64}{27}\)
7. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{3}{12}}\\= (\frac{81}{16})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{81}{16} }=\frac{3}{2}\)
8. \( \sqrt{ (\frac{3}{4})^{6} } \\= (\frac{3}{4})^{\frac{6}{2}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
9. \(\sqrt[9]{ (8)^{3} }\\= (8)^{\frac{3}{9}}\\= (8)^{\frac{1}{3}}\\=\sqrt[3]{ 8 }=2\)
10. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\\= (\frac{3}{4})^{\frac{-9}{3}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
11. \(\sqrt[4]{ (\frac{13}{15})^{-8} }\\= (\frac{13}{15})^{\frac{-8}{4}}\\= (\frac{13}{15})^{-2}\\= (\frac{15}{13})^{2}= \frac{225}{169}\)
12. \(\sqrt[4]{ (\frac{121}{169})^{2} }\\= (\frac{121}{169})^{\frac{2}{4}}\\= (\frac{121}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{121}{169} } =\frac{11}{13}\)