Getallen als grondtal

Hoofdmenu Eentje per keer  🖨

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

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

---

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

Verbetersleutel

1. \(\sqrt[4]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{4}}\\= (\frac{2}{3})^{3}=\frac{8}{27}\)
2. \(\sqrt[3]{ (\frac{1}{2})^{-9} }\\= (\frac{1}{2})^{\frac{-9}{3}}\\= (\frac{1}{2})^{-3}\\= (2)^{3}= 8\)
3. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\\= (\frac{3}{2})^{\frac{-16}{4}}\\= (\frac{3}{2})^{-4}\\= (\frac{2}{3})^{4}= \frac{16}{81}\)
4. \(\sqrt[4]{ (\frac{3}{8})^{-8} }\\= (\frac{3}{8})^{\frac{-8}{4}}\\= (\frac{3}{8})^{-2}\\= (\frac{8}{3})^{2}= \frac{64}{9}\)
5. \(\sqrt[12]{ (\frac{81}{16})^{3} }\\= (\frac{81}{16})^{\frac{-3}{12}}\\= (\frac{81}{16})^{\frac{-1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
6. \(\sqrt[8]{ (\frac{1}{16})^{4} }\\= (\frac{1}{16})^{\frac{4}{8}}\\= (\frac{1}{16})^{\frac{1}{2}}\\= \sqrt{ \frac{1}{16} } =\frac{1}{4}\)
7. \(\sqrt[3]{ (\frac{5}{6})^{-6} }\\= (\frac{5}{6})^{\frac{-6}{3}}\\= (\frac{5}{6})^{-2}\\= (\frac{6}{5})^{2}= \frac{36}{25}\)
8. \( \sqrt{ (2)^{6} } \\= (2)^{\frac{6}{2}}\\= (2)^{3}=8\)
9. \(\sqrt[3]{ (\frac{2}{3})^{12} }\\= (\frac{2}{3})^{\frac{12}{3}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
10. \(\sqrt[12]{ (\frac{27}{64})^{4} }\\= (\frac{27}{64})^{\frac{4}{12}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
11. \(\sqrt[4]{ (\frac{3}{2})^{16} }\\= (\frac{3}{2})^{\frac{16}{4}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
12. \(\sqrt[4]{ (\frac{64}{81})^{2} }\\= (\frac{64}{81})^{\frac{-2}{4}}\\= (\frac{64}{81})^{\frac{-1}{2}}\\= \sqrt{ \frac{81}{64} } =\frac{9}{8}\)