Getallen als grondtal

Hoofdmenu Eentje per keer  🖨

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

1. \(\sqrt[4]{ (\frac{2}{3})^{16} }\)
2. \(\sqrt[8]{ (\frac{16}{81})^{2} }\)
3. \(\sqrt[12]{ (\frac{27}{64})^{4} }\)
4. \(\sqrt[4]{ (\frac{3}{2})^{-16} }\)
5. \(\sqrt[8]{ (\frac{1}{4})^{4} }\)
6. \( \sqrt{ (\frac{2}{3})^{-4} } \)
7. \( \sqrt{ (\frac{3}{4})^{6} } \)
8. \(\sqrt[6]{ (\frac{324}{361})^{3} }\)
9. \(\sqrt[4]{ (\frac{3}{4})^{12} }\)
10. \( \sqrt{ (\frac{2}{3})^{8} } \)
11. \( \sqrt{ (\frac{2}{3})^{6} } \)
12. \(\sqrt[3]{ (\frac{1}{2})^{6} }\)

---

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

Verbetersleutel

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