Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{4} - \frac{5}{2} }= a^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ a^{15} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{4}|}\\---------------\)
  2. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
  3. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{6} - (\frac{-1}{2}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
  4. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
  5. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-2}{3}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
  6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-3}{2}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
  7. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
  8. \(\dfrac{a^{\frac{5}{6}}}{a^{-1}}\\= a^{ \frac{5}{6} - (-1) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
  9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{5}{2} - (\frac{-5}{4}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
  10. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
  11. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{2}) }= q^{0}\\=1\\---------------\)
  12. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{5} - \frac{1}{4} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:20:47