Getallen als grondtal

Hoofdmenu Eentje per keer  🖨

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

1. \(\sqrt[12]{ (\frac{1}{8})^{4} }\)
2. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\)
3. \(\sqrt[8]{ (\frac{289}{400})^{4} }\)
4. \(\sqrt[6]{ (\frac{100}{169})^{3} }\)
5. \( \sqrt{ (\frac{3}{2})^{8} } \)
6. \(\sqrt[8]{ (\frac{16}{361})^{4} }\)
7. \(\sqrt[3]{ (\frac{11}{16})^{6} }\)
8. \(\sqrt[6]{ (\frac{27}{64})^{2} }\)
9. \(\sqrt[12]{ (\frac{16}{81})^{3} }\)
10. \( \sqrt{ (\frac{4}{19})^{4} } \)
11. \(\sqrt[9]{ (\frac{8}{27})^{3} }\)
12. \(\sqrt[6]{ (\frac{1}{8})^{2} }\)

---

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

Verbetersleutel

1. \(\sqrt[12]{ (\frac{1}{8})^{4} }\\= (\frac{1}{8})^{\frac{-4}{12}}\\= (\frac{1}{8})^{\frac{-1}{3}}\\=\sqrt[3]{ 8 }=2\)
2. \(\sqrt[3]{ (\frac{3}{4})^{-9} }\\= (\frac{3}{4})^{\frac{-9}{3}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
3. \(\sqrt[8]{ (\frac{289}{400})^{4} }\\= (\frac{289}{400})^{\frac{4}{8}}\\= (\frac{289}{400})^{\frac{1}{2}}\\= \sqrt{ \frac{289}{400} } =\frac{17}{20}\)
4. \(\sqrt[6]{ (\frac{100}{169})^{3} }\\= (\frac{100}{169})^{\frac{3}{6}}\\= (\frac{100}{169})^{\frac{1}{2}}\\= \sqrt{ \frac{100}{169} } =\frac{10}{13}\)
5. \( \sqrt{ (\frac{3}{2})^{8} } \\= (\frac{3}{2})^{\frac{8}{2}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
6. \(\sqrt[8]{ (\frac{16}{361})^{4} }\\= (\frac{16}{361})^{\frac{4}{8}}\\= (\frac{16}{361})^{\frac{1}{2}}\\= \sqrt{ \frac{16}{361} } =\frac{4}{19}\)
7. \(\sqrt[3]{ (\frac{11}{16})^{6} }\\= (\frac{11}{16})^{\frac{6}{3}}\\= (\frac{11}{16})^{2}=\frac{121}{256}\)
8. \(\sqrt[6]{ (\frac{27}{64})^{2} }\\= (\frac{27}{64})^{\frac{2}{6}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
9. \(\sqrt[12]{ (\frac{16}{81})^{3} }\\= (\frac{16}{81})^{\frac{3}{12}}\\= (\frac{16}{81})^{\frac{1}{4}}\\=\sqrt[4]{ \frac{16}{81} }=\frac{2}{3}\)
10. \( \sqrt{ (\frac{4}{19})^{4} } \\= (\frac{4}{19})^{\frac{4}{2}}\\= (\frac{4}{19})^{2}=\frac{16}{361}\)
11. \(\sqrt[9]{ (\frac{8}{27})^{3} }\\= (\frac{8}{27})^{\frac{3}{9}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
12. \(\sqrt[6]{ (\frac{1}{8})^{2} }\\= (\frac{1}{8})^{\frac{2}{6}}\\= (\frac{1}{8})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{1}{8} }=\frac{1}{2}\)