Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer 

Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
  2. \(\dfrac{q^{\frac{-1}{3}}}{q^{-2}}\\= q^{ \frac{-1}{3} - (-2) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
  3. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
  4. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{4} - \frac{1}{5} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
  5. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
  6. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
  7. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{4}{5} - (\frac{-3}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
  8. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{5}{3} - \frac{3}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
  9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{6} - \frac{5}{6} }= q^{0}\\=1\\---------------\)
  10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{2} - \frac{4}{5} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
  11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
  12. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{3} - \frac{3}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-29 20:59:16
Een site van Busleyden Atheneum Mechelen