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Werk uit m.b.v. de rekenregels

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

Werk uit m.b.v. de rekenregels

Verbetersleutel

  1. \(x^{\frac{-1}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{-1}{5} + \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
  2. \(a^{-1}.a^{\frac{-3}{2}}\\= a^{ -1 + (\frac{-3}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
  3. \(x^{\frac{-1}{2}}.x^{\frac{-3}{5}}\\= x^{ \frac{-1}{2} + (\frac{-3}{5}) }= x^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[10]{ x }}=\frac{1}{|x|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{2}|}\\---------------\)
  4. \(y^{\frac{1}{2}}.y^{1}\\= y^{ \frac{1}{2} + 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
  5. \(x^{\frac{-3}{5}}.x^{\frac{-1}{4}}\\= x^{ \frac{-3}{5} + (\frac{-1}{4}) }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)
  6. \(a^{\frac{1}{5}}.a^{\frac{-3}{2}}\\= a^{ \frac{1}{5} + (\frac{-3}{2}) }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
  7. \(a^{-2}.a^{-1}\\= a^{ -2 + (-1) }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
  8. \(q^{\frac{5}{2}}.q^{\frac{-2}{3}}\\= q^{ \frac{5}{2} + (\frac{-2}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
  9. \(y^{\frac{3}{2}}.y^{\frac{3}{5}}\\= y^{ \frac{3}{2} + \frac{3}{5} }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
  10. \(y^{\frac{-1}{5}}.y^{\frac{-1}{2}}\\= y^{ \frac{-1}{5} + (\frac{-1}{2}) }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
  11. \(y^{\frac{-5}{3}}.y^{\frac{-1}{3}}\\= y^{ \frac{-5}{3} + (\frac{-1}{3}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
  12. \(q^{\frac{-1}{4}}.q^{\frac{5}{2}}\\= q^{ \frac{-1}{4} + \frac{5}{2} }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:07:09