Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

  1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\)
  2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{4}}}\)
  3. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{3}}}\)
  4. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{2}{3}}}\)
  5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\)
  6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\)
  7. \(\dfrac{x^{\frac{2}{3}}}{x^{2}}\)
  8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{2}}}\)
  9. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{1}{3}}}\)
  10. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\)
  11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{3}}}\)
  12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{6}}}\)

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
  2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{3}{5} - (\frac{-5}{4}) }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)
  3. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{5} - (\frac{-1}{3}) }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
  4. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{4} - \frac{2}{3} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
  5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
  6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{2} - \frac{4}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
  7. \(\dfrac{x^{\frac{2}{3}}}{x^{2}}\\= x^{ \frac{2}{3} - 2 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
  8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
  9. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{3} - \frac{1}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
  10. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\\= a^{ -1 - (\frac{-5}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
  11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{3}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
  12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{3} - \frac{5}{6} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-19 14:22:27
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