Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer 

Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{4} - \frac{1}{4} }= y^{0}\\=1\\---------------\)
  2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{4}{5} - \frac{5}{2} }= a^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{7} }}=\frac{1}{|a|.\sqrt[10]{ a^{7} }} \color{purple}{\frac{\sqrt[10]{ a^{3} }}{\sqrt[10]{ a^{3} }}} \\=\frac{\sqrt[10]{ a^{3} }}{|a^{2}|}\\---------------\)
  3. \(\dfrac{x^{1}}{x^{\frac{1}{4}}}\\= x^{ 1 - \frac{1}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
  4. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
  5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-1}{2} - \frac{3}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
  6. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
  7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{3}{5} - (\frac{-2}{3}) }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
  8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-3}{5} - (\frac{-3}{4}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
  9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
  10. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{3}{2} - (\frac{-1}{5}) }= y^{\frac{17}{10}}\\=\sqrt[10]{ y^{17} }=|y|.\sqrt[10]{ y^{7} }\\---------------\)
  11. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{4}{3} - (\frac{-4}{5}) }= y^{\frac{32}{15}}\\=\sqrt[15]{ y^{32} }=y^{2}.\sqrt[15]{ y^{2} }\\---------------\)
  12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{2} - (\frac{-4}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-17 20:27:49
Een site van Busleyden Atheneum Mechelen