Rekenregels machten

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Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

  1. \((\frac{20}{11}a)^{-10}:(\frac{20}{11}a)^{-1}\)
  2. \((7a^{2})^{-8}\)
  3. \((\frac{19}{17}x)^{-5}.(\frac{19}{17}x)^{7}\)
  4. \((\frac{6}{5})^{10}.(\frac{2}{7})^{10}\)
  5. \((-\frac{3}{16})^{-5}\)
  6. \((13c)^{2}.(13c)^{6}\)
  7. \((\frac{3}{20})^{-2}.(\frac{15}{4})^{-2}\)
  8. \((\frac{3}{2}a)^{-9}.(\frac{3}{2}a)^{-10}\)
  9. \(-(-2)^{-2}\)
  10. \((-\frac{18}{17})^{-5}\)
  11. \((\frac{5}{8})^{9}.(\frac{8}{15})^{9}\)
  12. \((\frac{16}{5}y)^{7}:(\frac{16}{5}y)^{10}\)

Pas de correcte rekenregel(s) van machten toe [en reken uit indien mogelijk]

Verbetersleutel

  1. \((\frac{20}{11}a)^{-10}:(\frac{20}{11}a)^{-1}=(\frac{20}{11}a)^{-10-(-1)}=(\frac{20}{11}a)^{-9}=(\frac{11}{20}\frac{1}{a})^{9}\left[ =\frac{2357947691}{512000000000} \frac{1}{a^{9}} \right]\)
  2. \((7a^{2})^{-8}=(7)^{-8}.(a^{2})^{-8}=(\frac{1}{7})^{8}.(\frac{1}{a^{2}})^{8}\left[=\frac{1}{5764801} \frac{1}{a^{16}}\right]\)
  3. \((\frac{19}{17}x)^{-5}.(\frac{19}{17}x)^{7}=(\frac{19}{17}x)^{-5+7}=(\frac{19}{17}x)^{2}\left[=\frac{361}{289}x^{2}\right]\)
  4. \((\frac{6}{5})^{10}.(\frac{2}{7})^{10}=(\frac{6}{5}\frac{2}{7})^{10}=(\frac{12}{35})^{10}=\left[\frac{61917364224}{2758547353515625}\right]\)
  5. \((-\frac{3}{16})^{-5}=(-\frac{16}{3})^{5}=-\frac{16^{5}}{3^{5}}\left[=-\frac{1048576}{243}\right]\)
  6. \((13c)^{2}.(13c)^{6}=(13c)^{2+6}=(13c)^{8}\left[=815730721c^{8}\right]\)
  7. \((\frac{3}{20})^{-2}.(\frac{15}{4})^{-2}=(\frac{3}{20}\frac{15}{4})^{-2}=(\frac{9}{16})^{-2}=(\frac{16}{9})^{2}=\left[\frac{256}{81}\right]\)
  8. \((\frac{3}{2}a)^{-9}.(\frac{3}{2}a)^{-10}=(\frac{3}{2}a)^{-9+(-10)}=(\frac{3}{2}a)^{-19}=(\frac{2}{3}\frac{1}{a})^{19}\left[=\frac{524288}{1162261467} \frac{1}{a^{19}}\right]\)
  9. \(-(-2)^{-2}=-(-\frac{1}{2})^{2}=-\frac{1^{2}}{2^{2}}\left[=-\frac{1}{4}\right]\)
  10. \((-\frac{18}{17})^{-5}=(-\frac{17}{18})^{5}=-\frac{17^{5}}{18^{5}}\left[=-\frac{1419857}{1889568}\right]\)
  11. \((\frac{5}{8})^{9}.(\frac{8}{15})^{9}=(\frac{5}{8}\frac{8}{15})^{9}=(\frac{1}{3})^{9}=\left[\frac{1}{19683}\right]\)
  12. \((\frac{16}{5}y)^{7}:(\frac{16}{5}y)^{10}=(\frac{16}{5}y)^{7-10}=(\frac{16}{5}y)^{-3}=(\frac{5}{16}\frac{1}{y})^{3}\left[ =\frac{125}{4096} \frac{1}{y^{3}} \right]\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:39:40