Rekenregels machten

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

  1. \((\frac{4}{9})^{-9}.(5)^{-9}\)
  2. \((\frac{15}{7}b)^{10}:(\frac{15}{7}b)^{-5}\)
  3. \(-(-\frac{13}{12})^{-3}\)
  4. \((\frac{7}{6}b)^{-7}:(\frac{7}{6}b)^{5}\)
  5. \((\frac{5}{4})^{2}.(\frac{19}{3})^{2}\)
  6. \((-4)^{-2}\)
  7. \((\frac{17}{12})^{10}.(4)^{10}\)
  8. \((\frac{17}{9})^{-1}.(\frac{15}{16})^{-1}\)
  9. \((-\frac{3}{5})^{-6}\)
  10. \((-\frac{2}{3})^{-1}\)
  11. \((\frac{19}{13}b)^{1}.(\frac{19}{13}b)^{9}\)
  12. \((\frac{3}{14}x)^{5}.(\frac{3}{14}x)^{4}\)

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

Verbetersleutel

  1. \((\frac{4}{9})^{-9}.(5)^{-9}=(\frac{4}{9}5)^{-9}=(\frac{20}{9})^{-9}=(\frac{9}{20})^{9}=\text{ZRM}=\left[\frac{387420489}{512000000000}\right]\)
  2. \((\frac{15}{7}b)^{10}:(\frac{15}{7}b)^{-5}=(\frac{15}{7}b)^{10-(-5)}=(\frac{15}{7}b)^{15}=\text{ZRM}\left[ =\frac{437893890380859375}{4747561509943}b^{15} \right]\)
  3. \(-(-\frac{13}{12})^{-3}=-(-\frac{12}{13})^{3}=+\frac{12^{3}}{13^{3}}=\text{ZRM}\left[=\frac{1728}{2197}\right]\)
  4. \((\frac{7}{6}b)^{-7}:(\frac{7}{6}b)^{5}=(\frac{7}{6}b)^{-7-5}=(\frac{7}{6}b)^{-12}=(\frac{6}{7}\frac{1}{b})^{12}=\text{ZRM}\left[ =\frac{2176782336}{13841287201} \frac{1}{b^{12}} \right]\)
  5. \((\frac{5}{4})^{2}.(\frac{19}{3})^{2}=(\frac{5}{4}\frac{19}{3})^{2}=(\frac{95}{12})^{2}=\left[\frac{9025}{144}\right]\)
  6. \((-4)^{-2}=(-\frac{1}{4})^{2}=+\frac{1^{2}}{4^{2}}= \left[=\frac{1}{16}\right]\)
  7. \((\frac{17}{12})^{10}.(4)^{10}=(\frac{17}{12}4)^{10}=(\frac{17}{3})^{10}=\text{ZRM}=\left[\frac{2015993900449}{59049}\right]\)
  8. \((\frac{17}{9})^{-1}.(\frac{15}{16})^{-1}=(\frac{17}{9}\frac{15}{16})^{-1}=(\frac{85}{48})^{-1}=(\frac{48}{85})^{1}=\left[\frac{48}{85}\right]\)
  9. \((-\frac{3}{5})^{-6}=(-\frac{5}{3})^{6}=+\frac{5^{6}}{3^{6}}=\text{ZRM}= \left[=\frac{15625}{729}\right]\)
  10. \((-\frac{2}{3})^{-1}=(-\frac{3}{2})^{1}=-\frac{3^{1}}{2^{1}}= \left[=-\frac{3}{2}\right]\)
  11. \((\frac{19}{13}b)^{1}.(\frac{19}{13}b)^{9}=(\frac{19}{13}b)^{1+9}=(\frac{19}{13}b)^{10}\left[=\frac{6131066257801}{137858491849}b^{10}\right]=\text{ZRM}\)
  12. \((\frac{3}{14}x)^{5}.(\frac{3}{14}x)^{4}=(\frac{3}{14}x)^{5+4}=(\frac{3}{14}x)^{9}\left[=\frac{19683}{20661046784}x^{9}\right]=\text{ZRM}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:30:26