Bereken m.b.v. de rekenregels (zonder ZRM)
- \( \sqrt{ (\frac{17}{20})^{-4} } \)
- \(\sqrt[3]{ (\frac{3}{4})^{9} }\)
- \(\sqrt[6]{ (\frac{8}{27})^{2} }\)
- \( \sqrt{ (\frac{1}{2})^{6} } \)
- \(\sqrt[3]{ (\frac{3}{2})^{12} }\)
- \(\sqrt[3]{ (\frac{2}{3})^{-12} }\)
- \(\sqrt[4]{ (\frac{81}{196})^{2} }\)
- \( \sqrt{ (\frac{3}{4})^{-6} } \)
- \(\sqrt[9]{ (\frac{27}{64})^{3} }\)
- \( \sqrt{ (2)^{6} } \)
- \( \sqrt{ (\frac{2}{3})^{8} } \)
- \(\sqrt[6]{ (\frac{25}{196})^{3} }\)
Bereken m.b.v. de rekenregels (zonder ZRM)
Verbetersleutel
- \( \sqrt{ (\frac{17}{20})^{-4} } \\= (\frac{17}{20})^{\frac{-4}{2}}\\= (\frac{17}{20})^{-2}\\= (\frac{20}{17})^{2}= \frac{400}{289}\)
- \(\sqrt[3]{ (\frac{3}{4})^{9} }\\= (\frac{3}{4})^{\frac{9}{3}}\\= (\frac{3}{4})^{3}=\frac{27}{64}\)
- \(\sqrt[6]{ (\frac{8}{27})^{2} }\\= (\frac{8}{27})^{\frac{2}{6}}\\= (\frac{8}{27})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{8}{27} }=\frac{2}{3}\)
- \( \sqrt{ (\frac{1}{2})^{6} } \\= (\frac{1}{2})^{\frac{6}{2}}\\= (\frac{1}{2})^{3}=\frac{1}{8}\)
- \(\sqrt[3]{ (\frac{3}{2})^{12} }\\= (\frac{3}{2})^{\frac{12}{3}}\\= (\frac{3}{2})^{4}=\frac{81}{16}\)
- \(\sqrt[3]{ (\frac{2}{3})^{-12} }\\= (\frac{2}{3})^{\frac{-12}{3}}\\= (\frac{2}{3})^{-4}\\= (\frac{3}{2})^{4}= \frac{81}{16}\)
- \(\sqrt[4]{ (\frac{81}{196})^{2} }\\= (\frac{81}{196})^{\frac{2}{4}}\\= (\frac{81}{196})^{\frac{1}{2}}\\= \sqrt{ \frac{81}{196} } =\frac{9}{14}\)
- \( \sqrt{ (\frac{3}{4})^{-6} } \\= (\frac{3}{4})^{\frac{-6}{2}}\\= (\frac{3}{4})^{-3}\\= (\frac{4}{3})^{3}= \frac{64}{27}\)
- \(\sqrt[9]{ (\frac{27}{64})^{3} }\\= (\frac{27}{64})^{\frac{3}{9}}\\= (\frac{27}{64})^{\frac{1}{3}}\\=\sqrt[3]{ \frac{27}{64} }=\frac{3}{4}\)
- \( \sqrt{ (2)^{6} } \\= (2)^{\frac{6}{2}}\\= (2)^{3}=8\)
- \( \sqrt{ (\frac{2}{3})^{8} } \\= (\frac{2}{3})^{\frac{8}{2}}\\= (\frac{2}{3})^{4}=\frac{16}{81}\)
- \(\sqrt[6]{ (\frac{25}{196})^{3} }\\= (\frac{25}{196})^{\frac{-3}{6}}\\= (\frac{25}{196})^{\frac{-1}{2}}\\= \sqrt{ \frac{196}{25} } =\frac{14}{5}\)
Oefeningengenerator
vanhoeckes.be/wiskunde 2026-03-07 03:54:33