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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(y^{-2}.y^{\frac{-3}{2}}\\= y^{ -2 + (\frac{-3}{2}) }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
  2. \(x^{\frac{1}{2}}.x^{-1}\\= x^{ \frac{1}{2} + (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
  3. \(x^{-1}.x^{\frac{1}{3}}\\= x^{ -1 + \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
  4. \(a^{\frac{1}{4}}.a^{\frac{5}{3}}\\= a^{ \frac{1}{4} + \frac{5}{3} }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
  5. \(x^{\frac{1}{2}}.x^{\frac{2}{5}}\\= x^{ \frac{1}{2} + \frac{2}{5} }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
  6. \(q^{\frac{-1}{6}}.q^{-1}\\= q^{ \frac{-1}{6} + (-1) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
  7. \(y^{-1}.y^{\frac{3}{5}}\\= y^{ -1 + \frac{3}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
  8. \(x^{\frac{3}{2}}.x^{\frac{4}{3}}\\= x^{ \frac{3}{2} + \frac{4}{3} }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
  9. \(a^{-1}.a^{-1}\\= a^{ -1 + (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
  10. \(x^{\frac{2}{5}}.x^{1}\\= x^{ \frac{2}{5} + 1 }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
  11. \(y^{\frac{-3}{5}}.y^{\frac{-3}{2}}\\= y^{ \frac{-3}{5} + (\frac{-3}{2}) }= y^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ y^{21} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y }}=\frac{1}{|y^{2}|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{3}|}\\---------------\)
  12. \(y^{\frac{1}{2}}.y^{\frac{1}{2}}\\= y^{ \frac{1}{2} + \frac{1}{2} }= y^{1}\\\\---------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:14:32