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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(q^{\frac{3}{5}}.q^{\frac{-5}{4}}\\= q^{ \frac{3}{5} + (\frac{-5}{4}) }= q^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ q^{13} }}=\frac{1}{\sqrt[20]{ q^{13} }}. \color{purple}{\frac{\sqrt[20]{ q^{7} }}{\sqrt[20]{ q^{7} }}} \\=\frac{\sqrt[20]{ q^{7} }}{|q|}\\---------------\)
  2. \(x^{1}.x^{\frac{-4}{3}}\\= x^{ 1 + (\frac{-4}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
  3. \(x^{\frac{-1}{3}}.x^{\frac{3}{4}}\\= x^{ \frac{-1}{3} + \frac{3}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
  4. \(q^{\frac{1}{2}}.q^{\frac{-4}{5}}\\= q^{ \frac{1}{2} + (\frac{-4}{5}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
  5. \(y^{2}.y^{-1}\\= y^{ 2 + (-1) }= y^{1}\\\\---------------\)
  6. \(x^{\frac{5}{6}}.x^{\frac{-1}{5}}\\= x^{ \frac{5}{6} + (\frac{-1}{5}) }= x^{\frac{19}{30}}\\=\sqrt[30]{ x^{19} }\\---------------\)
  7. \(a^{2}.a^{\frac{-1}{2}}\\= a^{ 2 + (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
  8. \(y^{\frac{-1}{2}}.y^{-2}\\= y^{ \frac{-1}{2} + (-2) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
  9. \(a^{\frac{3}{2}}.a^{\frac{4}{5}}\\= a^{ \frac{3}{2} + \frac{4}{5} }= a^{\frac{23}{10}}\\=\sqrt[10]{ a^{23} }=|a^{2}|.\sqrt[10]{ a^{3} }\\---------------\)
  10. \(a^{\frac{5}{3}}.a^{\frac{3}{2}}\\= a^{ \frac{5}{3} + \frac{3}{2} }= a^{\frac{19}{6}}\\=\sqrt[6]{ a^{19} }=|a^{3}|.\sqrt[6]{ a }\\---------------\)
  11. \(x^{\frac{-5}{3}}.x^{\frac{1}{3}}\\= x^{ \frac{-5}{3} + \frac{1}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
  12. \(q^{\frac{-1}{2}}.q^{\frac{1}{2}}\\= q^{ \frac{-1}{2} + \frac{1}{2} }= q^{0}\\=1\\---------------\)
Oefeningengenerator wiskundeoefeningen.be 2025-07-31 10:44:51
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