Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-4}{3} - \frac{1}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
  2. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{6} - \frac{1}{2} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
  3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
  4. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
  5. \(\dfrac{q^{2}}{q^{\frac{-4}{5}}}\\= q^{ 2 - (\frac{-4}{5}) }= q^{\frac{14}{5}}\\=\sqrt[5]{ q^{14} }=q^{2}.\sqrt[5]{ q^{4} }\\---------------\)
  6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-4}{5}) }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
  7. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-5}{2} - \frac{5}{3} }= q^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ q^{25} }}\\=\frac{1}{|q^{4}|.\sqrt[6]{ q }}=\frac{1}{|q^{4}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{5}|}\\---------------\)
  8. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
  9. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{6} - \frac{5}{3} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
  10. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{4}) }= x^{0}\\=1\\---------------\)
  11. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
  12. \(\dfrac{y^{\frac{-2}{5}}}{y^{1}}\\= y^{ \frac{-2}{5} - 1 }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-04 03:17:01
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